万有理论

万有理论（英语：theory of everything）用来指那些试图统一自然界四种基本相互作用：万有引力、强相互作用、弱相互作用和电磁力成一体的理论。是在电磁力和弱相互作用力成一体的电弱作用统一理论和加入强相互作用成一体的大统一理论基础上，对统一自然界基本力的进一步努力。目前被认为最有可能成功的万有理论是M理论和超弦理论。

标准重力理论
重力理论的历史 · 牛顿重力（经典力学） · 广义相对论（历史 · |数学 · 资源 · 验证）
广义相对论的替代理论
古典重力理论 · 共形重力 · ECT理论 · 标量重力理论（Nordström重力理论 · Yilmaz重力理论） · 标量-张量理论（布兰斯-狄基理论 · 自我创造宇宙学） · 双度规理论 · 其他替代理论（爱因斯坦-嘉当理论 · 嘉当联络 · 怀海德重力理论 · 非对称重力理论 · 标量-张量-向量重力 · 张量-向量-标量重力）
统一场论
Teleparallelism · 几何动力学 · 量子引力（半古典重力 · 离散洛仑兹量子引力 · 欧几里得量子引力 · 引生重力 · 因果集 · 循环量子引力 · 惠勒-得卫特方程式） · 万有理论（超重力 · M理论 · 超弦理论 · 弦论）
其他
高维广义相对论（卡鲁扎-克莱因理论 · DGP模型）牛顿重力的替代理论（亚里斯多德重力理论 · Mechanical explanations · Le Sage重力理论 · MOND）
未分类
Composite gravity · Massive gravity

什么是物理理论?
?一、学科概况
?理论物理是从理论上探索自然界未知的物质结构、相互作用和物质运动的基本规律的学科。理论物理的研究领域涉及粒子物理与原子核物理、统计物理、凝聚态物理、宇宙学等，几乎包括物理学所有分支的基本理论问题。
?二、培养目标
?1．博士学位 应具备坚实的理论物理基础和广博的现代物理知识，了解理论物理学科的现状及发展方向，有扎实的数学基础，熟练掌握现代计算技术，能应用现代理论物理方法处理相关学科中发现的有关理论问题。具有独立从事科学研究的能力，具有严谨求实的科学态度和作风，在国际前沿方向或交错领域中有较深入的研究，并取得有创造性的成果。至少掌握一门外国语，能熟练地阅读本专业的外文资料，具有一定的写作能力和进行国际学术交流的能力。毕业后可独立从事前沿理论课题的研究，并能开辟新的研究领域。学位获得者应能胜任高等院校、科研院所及高科技企业的教学”研究、开发和管理工作。
?2．硕士学位 应有扎实的理论物理基础和相关的背景知识，了解理论物理学科的现状及发展方向，掌握研究物质的微观及宏观现象所用的模型和方法等专业理论以及相关的数学与计算方法，有严谨求实的科学态度和作风，具备从事前沿课题研究的能力。应较为熟练地掌握一门外国语，能阅读本专业的外文资料。毕业后能胜任高等院校、科研院所及高科技企业的教学、研究、开发和管理工作。
?三、业务范围
?1．学科研究范围 理论物理是在实验现象的基础上，以理论的方法和模型研究基本粒子、原子核、原子、分子、等离子体和凝聚态物质运动的基本规律，解决学科本身和高科技探索中提出的基本理论问题。研究范围包括粒子物理理论、原子核理论、凝聚态理论、统计物理、光子学理论、原子分子理论、等离子体理论、量子场论与量子力学、引力理论、数学物理、理论生物物理、非线性物理、计算物理等。
?2．课程设置 高等量子力学、高等统计物理、量子场论、群论、规范场论、现代数学方法、计算物理、凝聚态理论、量子多体理论、粒子物理、核理论、非平衡统计物理、非线性物理、广义相对论、量子光学、理论生物物理、天体物理、微分几何、拓扑学等。
?四、主要相关学科
?粒子物理与原子核物理，原子和分子物理，凝聚态物理，等离子体物理，声学，光学，无线电物理，基础数学，应用数学，计算数学，凝聚态物理，化学物理，天体物理，宇宙学，材料科学，信息科学和生命科学

－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－
目前主要研究方向：
(一)、粒子物理和量子场论
粒子物理学是研究物质微观结构及基本相互作用规律的物理学前沿学科。粒子物理理论作为量子场的基本理论，取得了极大的成功。粒子物理标准模型的建立是二十世纪物理学的重大成就之一，它能统一描述目前人类已知的最小"粒子"（夸克、轻子、光子、胶子、中间玻色子、Higgs 粒子）的性质及强、电、弱三种基本相互作用。粒子物理学有许多研究方向，例如：强子物理、重味物理、轻子物理、中微子物理、标准模型精确检验、对称性和对称性破坏、标准模型扩展等等。
当前，该所开展的粒子物理理论研究主要围绕粒子物理标准模型中尚未解决的一些基本问题和有关实验所暗示的新物理进行。其主要内容为：电弱对称性破缺机制，CP破坏和费米子质量起源，太阳和大气中微子失踪之谜以及粒子物理中的一些重要问题，量子色动力学的低能动力学，量子味动力学，手征微扰理论，重味夸克有效场论，手征对称性和夸克禁闭，格点规范理论，重味物理，中微子物理，强子结构和性质，超高能碰撞等。研究中特别注意各种新理论和新模型，如：超对称理论和模型，超对称大统一模型，两个或多个Higgs模型，味对称规范模型。在研究方式上注重紧密与实验结合，并以实验为基础，探索超出标准模型的新理论和新模型以及新的物理概念，运用和发展量子场论、群论、数学物理和计算物理等理论物理方法，开展与粒子物理前沿相关的量子场论研究。此外，重视与其他学科的交叉，开展粒子天体物理，粒子宇宙学和粒子核物理以及与粒子物理有关的超弦理论唯象学的研究。

(二)、超弦理论和场论
量子场论是研究微观世界的基本工具，属于重要的前沿领域，它的研究成果直接地影响理论物理许多分支领域的进展。弦理论是在量子场论基础上发展起来的一种新的物理模型，它避免了通常场论中遇到的紫外发散等问题，是当前统一四种相互作用理论的重要尝试。
目前该所在此方向的研究课题为：
1、量子场论及超弦理论，特别是其非微扰问题；弦理论的最新发展；
2、场论（特别是规范场论）及弦理论的数学工具，包括非对易几何，几何量子化等以及非对易空间上的规范场论、离散群或离散点集上规范场论、用非线性联络的规范场论等。
3、各种数学物理和计算物理问题；
4、低维场论，特别是与低维凝聚态物理有关的场论；
5、与粒子物理相联系的量子场论问题；弦理论在粒子物理中的应用；
6、与引力理论相关的量子场论问题，包括源于弦理论的量子引力、黑洞熵的起源等等。

(三)、引力理论与宇宙学
爱因斯坦的广义相对论是一个十分成功的经典引力理论,将引力量子化从而 建立一个自恰的量子引力理论是当前理论物理的一大重要任务。与广义相对论相比，标量－张量引力论具有很强的竞争力。广义相对论在宇宙学及天体物理中的应用（包括大爆炸宇宙模型、中子星和黑洞、引力透镜以及引力波的预言）已取得巨大成功，但是，许多疑难问题有待解决。例如，奇性困难，暗物质的构成及其存在形式、物理性质、在宇宙中的占有比例及其对宇宙演化的作用，物质反物质的不对称性，宇宙常数和暗能量问题，原初核合成，宇宙早期相变过程的拓扑缺陷问题,宇宙早期暴涨模型的建立,黑洞的量子力学,引力的全息性质等。
国际上若干大型的空间和地面天文观测装置（包括大型望远镜、引力波天文台、等效原理的检验装置等等）将在今后若干年内投入使用，这将对现有的宇宙学模型、引力波的预言以及等效原理的正确性提供更精确的检验，随之而来的将是宇宙学和引力论的迅速发展，为理论工作提供更多获取重要成果的机遇。
理论物理所在本方向的研究围绕上述疑难问题开展。 (四)、凝聚态理论和计算凝聚态物理
复杂性和多样性是多体微观量子世界的基本特征，对其规律性的探索是凝聚态理论研究的核心。这方面的每一次突破，例如能带论和超导的BCS理论的建立，都对量子多体物理的应用和微观世界的认识产生了深刻的变革，其成果交叉渗透到数学、化学、材料、信息、计算机等许多学科和领域。近年来，在陶瓷材料、半导体异质结及其它低维固体材料中发现的大量反常物理现象***着新的电子论的诞生。对这些新的物理现象的研究是该所研究人员的一个中心任务，主要的研究方向包括：
量子Hall效应、高温超导电性、巨磁阻等强关联系统的物理机理、量子液体及量子临界现象；
量子多体理论方法，特别是数值计算的方法的探索和应用。计算方法包括密度矩阵重整化群、量子蒙特-卡罗计算、从头计算等；
量子点、线、碳管等纳米材料、半导体材料或结构中的非平衡量子输运及自旋电子学；
格点系统中的量子反散射与可积问题研究。

(五)、统计物理与理论生命科学
统计物理学研究方法极为普遍，研究对象广泛，它是微观到宏观的桥梁，简单到复杂的阶梯，理论到应用的途径。从生物大分子序列分析，到认识其空间结构，到理解生命活动中的物理化学过程，生命科学提出了大量富有挑战性的统计物理问题。这些问题的研究将深化对生命现象本质的认识，同时也将促进统计物理学本身的发展。
该所过去在本研究方向上重点开展了相变理论与临界现象、非线性动力学等方面的研究，目前研究重点集中在有限系统临界现象、重整化群方法、生物大分子序列分析以及生物体系中的输运问题等方面，探讨由生命科学激发的具有普遍意义的统计物理问题。生物信息学研究是本方向的热点，该所研究人员与北京华大基因研究中心有很密切的合作关系，在水稻基因组研究工作中已作出重要创新性成果。

(六)、理论生物物理
双亲分子膜是凝聚态物理软物质，或者叫复杂流体的前沿研究对象，是物理、化学、生物学交叉学科的研究课题。该所研究人员主要是运用微分几何方法，以液晶为模型，研究双亲分子膜的形状及其相变问题，已作出一组有国际影响的工作。现在本方向的研究正在向单分子膜、生物大分子与它们的生物功能联系（DNA单分子弹性、蛋白质折叠等）的理论探索扩展。

(七)、原子核理论
从20世纪九十年代中期开始到本世纪初的十年内，国际上先后有一批超大型核物理实验装置投入运行，如TJNAF(CEBAF)，RIB，RHIC 等等，核物理的发展进入了一个新阶段。这些新的巨型装置为从更深入的层次上研究核子－核子相互作用、核内的短程行为和核结构、各种极端条件下的核现象、核性质和多体理论方法提供了很好的机遇。在未来十年中，该所的研究人员将集中力量开展超重元素的性质及其合成途径，极端条件下的原子核结构，核天体物理及核内夸克效应等方面的研究，以求得对原子核运动规律的新认识。

(八)、量子物理、量子信息和原子分子理论
目前高技术的发展使得以前无法得到的极端物理条件（如极端强场、超低温度和可控的介观尺度）在实验室中得以实现。在这些特殊条件下，物质与光场的相互作用过程会呈现出一系列全新的物理现象,使得人们能重新认识物理学基本问题，导致新兴学科分支（如量子信息）的建立。
量子信息是以量子力学基本原理为基础、充分利用量子相干的独特性质(量子并行和量子纠缠)，探索以全新的方式进行计算、编码和信息传输的可能性，为突破芯片元件尺度的极限提供新概念、新思路和新途径。量子力学与信息科学结合,充分显示了学科交叉的重要性，可能会导致信息科学观念和模式的重大变革。该所本方向的研究将基于量子物理基本问题的理论和最新实验的结合, 鼓励学科间的交叉渗透。发挥理论物理对量子信息研究具有前瞻性和指导性的作用，瞄准国际前沿，立足思想创新、探索和解决当前量子信息前沿领域的关键理论性问题。
目前该所在此方向上的研究课题主要为:
1．量子测量和量子开系统的基本问题:包括量子系统与经典系统相互作用，量子到经典过渡的基本模型,微观信息宏观提取的理论机制，量子耗散和量子退相干理论；也包括发展和应用实际的量子测量理论，探讨提高探测量子态效率的可能性。
2. 特殊量子态的基本特性。包括研究各种宏观量子态（原子玻色－爱因斯坦凝聚和原子激光，介观电流，微腔激子-极化子）的基本特性和运动规律,并探索它们作为量子信息载体的可能性.也包括超冷囚禁原子、分子系统与受限光场的相互作用，如腔量子电动力学和原子光学。
3．量子信息方案的物理基础。包括演化过程的动力学控制、纠缠态的度量，多粒态的局域制备和纯化、已知量子态远程制备和未知量子态远程传输。还包括提出新的量子算法、量子编码和量子纠错的新型方案，研究量子信息中的计算复杂性理论和相应的各种数学物理问题。
4. 强场中的原子分子运动。主要兴趣集中在强磁场和强激光场中原子分子的动力学行为，其中，许多全新的实验现象要求发展处理非微扰问题的崭新概念和方法。这方面的研究对揭示混沌体系的动力学和利用外场控制分子、原子过程有着重要意义。

(九)、计算物理
辛算法和保结构算法是我国著名数学家冯康及其学派在80年代中期系统提出、并完善和发展起来的。他们在这个领域的工作不仅一直领先，而且在计算数学领域占有非常重要的地位并取得了国际上的公认。在计算数学和计算物理中，引入保持所计算的Hamilton系统的辛结构，或者对于接触系统等保持系统有关的几何结构的思想非常重要。最近，国际上沿着保结构的思想，有关领域又有新的进展。比如多辛算法和李群算法的提出等等，它们分别是保持无限维系统的多辛结构的算法和系统李群对称性的算法。
该所在本研究方向上研究辛算法、多辛算法等各种保结构算法 及其在物理中的应用。

http://zh.wikipedia.org/wiki/%E5%BC%95%E5%8A%9B%E6%B3%A2
引力波

http://zh.wikipedia.org/wiki/%E5%BC%95%E5%8A%9B%E5%AD%90
引力子

http://en.wikipedia.org/wiki/Polyakov_action
Polyakov action

Symmetries in physics can be global symmetries or local symmetries. These are defined as follows:
• A global symmetry is one that holds at all points in space-time. The parameters of the transformation will not depend on space-time.
• A local symmetry is one that acts differently at different space-time points.
In this case, the parameters of the transformation will be functions of the space-time coordinates.
You should recall from your studies of classical mechanics and quantum field theory that a symmetry in physics leads to a conservation law. The formal statement of this fact is called Noether’s theorem.

http://zh.wikipedia.org/wiki/%E5%82%85%E7%AB%8B%E5%8F%B6%E5%8F%98%E6%8D%A2%E5%AE%B6%E6%97%8F%E4%B8%AD%E7%9A%84%E5%85%B3%E7%B3%BB
傅立叶变换家族中的关系

http://zh.wikipedia.org/wiki/%E7%8B%84%E6%8B%89%E5%85%8B%CE%B4%E5%87%BD%E6%95%B0
狄拉克δ函数

Quantization

to quantize the string: the
covariant approach and light-cone quantization. Each offers its advantages.
Covariant quantization makes Lorentz invariance manifest but allows for the
existence of “ghost states” (states with negative norm) in the theory. In contrast,
light-cone quantization is ghost free. However, Lorentz invariance is no longer
obvious. Another trade-off is that the proof of the number of space-time dimensions
(D = 26 for the bosonic theory) is rather diffi cult in covariant quantization, but it’s
rather straightforward in light-cone quantization. Finally identifying the physical
states is easier in the light-cone approach.
Another method of quantization, that in some ways is a more advanced approach,
is called BRST quantization. This approach takes a middle ground between the two
methods outlined above. BRST quantization is manifestly Lorentz invariant, but
includes ghost states in the theory. Despite this, BRST quantization makes it easier
to identify the physical states of the theory and to extract the number of space-time
dimensions relatively easily.
Copyright

No-Ghost Theorem
The no-ghost theorem is simply a statement of the results we have seen in Chap. 4
and here, namely, that if the number of space-time dimensions is given by D = 26,
then negative norm states are eliminated from the theory.
Summary
In this chapter we introduced the BRST formalism and illustrated how it can be used
to quantize strings. This is a more sophisticated approach than covariant quantization
or light-cone quantization. It takes a middle ground, preserving manifest Lorentz
invariance while living with ghost states. The approach makes the appearance of the
critical D = 26 dimension simple to understand.

T-Duality for Closed Strings

T-duality is a symmetry which exists between different string theories. This
symmetry relates small distances in one theory to large distances in another,
seemingly different theory and shows that the two theories are in fact the same
theory expressed from different viewpoints. This is an important recognition; before
T-duality was discovered it was believed that there were fi ve different string
theories, when in fact they were all different versions of the same theory that could
be related to one another by transformations or dualities. One can transform between
small and large distances when considering the compactifi ed dimension in one
theory, and arrive at another dual theory. This is the essence of T-duality. We will
see later that other dualities exist in string theory as well.


Summarizing
• T-duality transforms Neumann boundary conditions into Dirichlet boundary
conditions.
• T-duality transforms Dirichlet boundary conditions into Neumann boundary
conditions.
• T-duality transforms a bosonic string with momentum but no winding into a
string with winding but no momentum.
• For the dual string, the string endpoints are restricted to lie on a 25-dimensional
hyperplane in space-time.
• The endpoints of the dual string can wind the circular dimension an integer
number of times given by K.

D-Branes
The hyperplane that the open string is attached to carries special signifi cance. A
D-brane is a hypersu***ce in space-time. In the examples worked out in this chapter,
it is a hyperplane with 24 spatial dimensions. The dimension which has been
excluded in this example is the dimension which has been compactifi ed. The D is
short for Dirichlet which refers to the fact that the open strings in the theory have endpoints that satisfy Dirichlet boundary conditions. In English this means that the
endpoints of an open string are attached to a D-brane.
A D-brane can be classifi ed by the number of spatial dimensions it contains. A point
is a zero-dimensional object and therefore is a D0-brane. A line, which is a onedimensional
object is a D1-brane (so strings can be thought of as D1-branes). Later we
will see that the physical world of three spatial dimensions and one time dimension that
we can perceive directly is a D3-brane contained in the larger world of 11-dimensional
hyperspace. In the example studied in this chapter, we considered a D24-brane, with one
spatial dimension compactifi ed that leaves 24 dimensions for the hyperplane su***ce.
Using the procedure outlined here, other dimensions can be compactifi ed. If we
choose to compactify n dimensions then that leaves behind a D(25-n)-brane. The
procedure outlined here is essentially the same in superstring theory, but in that
case compactifying n dimensions gives us a D(9-n)-brane. Note that:
• The ends of an open string are free to move in the noncompactifi ed
directions—including time. So in bosonic theory, if we have compactifi ed
n directions, the endpoints of the string are free to move in the other
1 + (25-n) directions. In superstring theory, the endpoints will be free to
move in the other 1 + (9-n) directions. In the example considered in this
chapter where we compactifi ed 1 dimension in bosonic string theory, the
end points of the string are free to move in the other 1 + 24 dimensions.
We can consider the existence of D-branes to be a consequence of the symmetry
of T-duality. The number, types, and arrangements of D-branes restrict the open
string states that can exist. We will have more to say about D-branes and discuss
T-duality in the context of superstrings in future chapters.

A Summary of Superstring Theory
Before jumping into some mathematical details about heterotic string theory, let’s
review the basic structure of string theory. This is a good idea because there are
several string theories with different states of the string. Five of the theories are superstring theories, and we also saw that it is possible to construct a theory
consisting only of bosons. Actually you can list four different bosonic string
theories, which we will do here.

BOSONIC STRING THEORY
We began our look at strings by considering bosonic string theory. This is an
unrealistic theory because we know that the real world contains particles that are
fermions. Nonetheless bosonic string theory provides an easier framework that can
be used to illustrate the key ideas and techniques of string theory.
Some key aspects of bosonic string theory you should remember are
• It introduces the concept of extra spatial dimensions. In order to avoid
ghosts (states with negative norm) we were forced to accept that there are
26 space-time dimensions.
• The ground state (the lowest energy or lowest excitation mode of the string)
has a negative mass-squared (m2 = −1/α ′ ). This state is called a tachyon.
The presence of a tachyon in the theory indicates that the ground state
or vacuum is unstable. Note that in relativity, tachyons are particles that
travel faster than the speed of light. Therefore the tachyon is a physically
unrealistic particle. There is no known way to remove tachyon states from
bosonic string theory.
• Bosonic string theory always includes gravity. This is indicated by the
presence of a spin-2 state called the graviton. This is a hint that string theories
provide a framework for the unifi cation of all known physical interactions.
• Bosonic string theories also include a state called the dilaton. This is a
scalar fi eld which is denoted byϕ . It is related to the coupling constant g
via g = exp< ϕ> , where< ϕ> is the vacuum expectation value of the dilaton
fi eld. If you need to brush up on your quantum fi eld theory, note that the
coupling constant determines the strength of an interaction. The dilaton
fi eld is dynamical (it is space-time dependent), so in string theory we obtain
a dramatic result that the string coupling constant can be dynamical. The
dilaton is also known as the gravitational scalar fi eld and may play a role
in the recently discovered nonzero cosmological constant.
Strings can be either open or closed and can be oriented or unoriented. If a string
is oriented, this means that directions along the string are unequivalent. So you can
tell which way you’re going along the string. By choosing open or closed strings
and oriented or unoriented strings, we can actually construct four different bosonic
string theories.

If a bosonic string theory has open strings, it automatically includes closed
strings as well. This is due to the dynamical behavior of strings. If a string is open,
it is possible for the endpoints to join together, forming a closed string state. Let’s
summarize the four possibilities for bosonic string theory.
If a bosonic string theory only includes closed strings that are oriented, then the
spectrum of the theory includes the following states:
• Tachyon
• Massless antisymmetric tensor
• Dilaton
• Graviton
Now, suppose that we only have closed strings, but the theory describes unoriented
strings instead. That is, we can’t tell which direction we are moving along the string.
In this case, the theory no longer includes a massless vector boson. We can summarize
the key aspects of the spectrum as
• Tachyon
• Dilaton
• Massless state which is the graviton
Now let’s turn to bosonic string theories that include open as well as closed
strings. Again, we can choose strings that are oriented and strings that are unoriented.
The oriented theory is characterized by
• Tachyon
• Dilaton
• Graviton
• A massless antisymmetric tensor
The closed string and open string tachyons are distinct. Choosing oriented open
+ closed bosonic string theory gives us
• Tachyon
• Dilaton
• Massless graviton
There is also a massless vector state for open strings, which can be oriented or
unoriented. So we see that all bosonic string theories are plagued by the presence of
a tachyon state. They have an unstable vacuum and do not include fermions. As a
result, we are forced to consider superstring theories.

Superstring Theory

Superstring theory is a generalization of bosonic string theory which extends the theory
to include fermions. There are fi ve different superstring theories. We use the word super
in our description of them because all fi ve theories are based on a theory of physics
known as supersymmetry. This theory is characterized by the idea that each fermion has
a bosonic partner and vice versa. Some examples are given in Table 10.1.
The existence of supersymmetry is a good indirect test of string theory. For string
theory to be true, supersymmetry must exist in nature. At the time of writing no
super-partner has ever been discovered, so supersymmetry either doesn’t exist in
nature or it has been broken. One way it could be broken is that the superpartners
are extremely massive. This means it would take high energies to see them. The
Large Hadron Collider (LHC) set to begin operation in 2008 may be powerful
enough to detect supersymmetry.
So, superstring theory includes supersymmetry, which allows us to introduce
fermions into the theory. It also includes ghost states, which are removed in an
analogous, manner to what we saw in bosonic string theory. When the ghost states
are removed we arrive at the second general characteristic of superstring theory:
• There are 10 space-time dimensions.
There are two ways to introduce supersymmetry into string theory, reviewed in
Chaps. 7 and 9, respectively:
• The RNS formalism adds supersymmetry to the worldsheet.
• The GS formalism adds supersymmetry to space-time.
We can still characterize superstring theories by noting whether or not they
include open and/or closed strings, and whether those strings are oriented or
unoriented. In addition, a superstring theory can be characterized by the number of
supercharges used in the theory. This is done by saying that a theory with N = m supercharges has N = m supersymmetry. Finally, we can characterize each
superstring theory by the gauge symmetry that it admits. All superstring theories
eliminate the tachyon from the spectrum and include a graviton, so superstring
theory naturally describes gravity.
TYPE I SUPERSTRING THEORY
Type I superstring theory can be characterized as follows:
• It includes both open and closed strings.
• It describes unoriented strings.
• It has N = 1 supersymmetry.
• It has SO(32) gauge symmetry.
In addition, type I superstrings can have charges attached to their ends called
Chan-Paton factors, a topic we will explore in a later chapter.
TYPE II A
Type II A theory describes closed, oriented superstrings. We can summarize the
theory as follows:
• It only includes closed strings.
• It has N = 2 supersymmetry.
• It has a U(1) gauge symmetry.
Since this theory only has a U(1) gauge symmetry, it is not large enough to
describe all the particle states seen in nature. It can describe gravity and
electromagnetism, but cannot describe the weak or strong forces. The theory has
two supercharges, and Θ1 and Θ2 have opposite chirality. Practically speaking, this
means that each fermion has a partner state with opposite chirality.
TYPE II B
Type II B theory also describes closed strings, also oriented. Although it includes
fermionic states because it is a superstring theory, it has no gauge symmetry and so
can only describe gravity. Like type II A theory, it has N = 2 supersymmetry, but
Θ1 and Θ2 have the same chirality. This remedies the diffi culty in type II A theory
in that the fermions described in type II B theory do not have partners of opposite
chirality. But the lack of a gauge group indicates the theory cannot be the whole
story as far as a unifi ed theory of physics.

HETEROTIC SO(32)
There are two heterotic theories that both describe closed, oriented strings. A heterotic
theory is a kind of fusion between bosonic and superstring theory. The left movers
and right movers are treated using different theories. We describe modes moving in
one direction using bosonic string theory, and describe the modes moving in the
opposite direction using N = 1 supersymmetry. The extra 16 dimensions of the bosonic
theory are regarded as abstract, mathematical entities rather than actual space-time
coordinates (like superspace). There are two heterotic theories, both with large gauge
groups that can describe all particles in nature. The fi rst has SO(32).
HETEROTIC E8 × E8
Similar to Heterotic SO(32) theory but has the gauge group E8xE8 .

Dualities
The state of string theory at this point appears to be a random mess, but the discovery
of a set of dualities which relate the fi ve theories amongst themselves saved the day.
The fact is that the fi ve theories are all related to one another, and we can transform
between them. This has led physicists to believe that there exists an underlying
theory. The fi ve superstring theories arise as different aspects or solutions of the
underlying theory. While some aspects of the potentially underlying theory have
been characterized, the actual underlying theory remains unknown. It goes by the
name of M-theory.
T-DUALITY
We have already studied one duality in detail in Chap. 8, T-duality. To review Tduality
relates a theory with a small compact dimension to a theory where that same
dimension is large. T-duality relates string theories as follows:
• It relates type II A and type II B theory.
• It relates the two heterotic theories.
T-duality can be summarized by saying that if we transform from a small to a
large distance scale we exchange momentum and winding modes (and vice versa).
T-duality relates type II A and type II B theory in that if we move from small to
large distance in type II A theory, the theory is transformed into type II B theory and vice versa (or switch momentum and winding modes). The same holds for the two
heterotic theories. This means that type II A and type II B are really the same theory,
and the two heterotic theories are really the same theory.
S-DUALITY
The second big duality that has been discovered is S-duality. Remember that a coupling
constant determines the strength of an interaction, and in string theory the dilaton
fi eld determines the value of the coupling constant. String theories have different
coupling constants that are weak or strong. By letting ϕ →−ϕ where ϕ is the dilaton
fi eld, since the coupling constant is defi ned from g = exp <ϕ >, we see that we can
transform a large coupling constant into a small one and vice versa, changing a strong
interaction into a weak one and vice versa. This is what S-duality is about. S-duality
brings type I superstring theory into the fold. That is, under S-duality
• Type I superstring theory is related to heterotic SO(32) superstring theory.
• Type II B is S-dual to itself.
So, a strong interaction in Type I superstring theory is the same as a weak
interaction in heterotic SO(32) theory, and vice versa. In other words, the two
theories are really the same theory at different coupling strengths.

Table 10.1 A listing of some particles and their postulated super-partners.
Partner Superpartner
Photon (spin 1) Photino (spin 1/2)
Graviton (spin 2) Gravitino (spin 3/2)
Quark (spin 1/2) Squark (spin 0)
Electron (spin 1/2) Selectron (spin 0)
Gluon (spin 0) Gluino (spin 1/2)

Higgs Mechanism
As the standard model of particle physics is formulated, the masses of all the
particles are 0. An extra fi eld called the Higgs fi eld has to be inserted by hand to
give the particles mass. The quantum of the Higgs fi eld is a spin-0 particle called
the Higgs boson. The Higgs boson is electrically neutral.
The Higgs fi eld, if it exists, is believed to fi ll all of empty space throughout the
entire universe. Elementary particles acquire their mass through their interaction
with the Higgs fi eld. Mathematically we introduce mass into a theory by adding
interaction terms into the Lagrangian that couple the fi eld of the particle in question
to the Higgs fi eld. Normally, the lowest energy state of a fi eld would have an
expectation value of zero. By symmetry breaking, we introduce a nonzero lowest
energy state of the fi eld. This procedure leads to the acquisition of mass by the
particles in the theory.
Qualitatively, you might think of the Higgs fi eld by imagining the differences
between being on land and being completely submerged in water. On dry land, you
can move your arm up and down without any trouble. Under water, moving your
arm up and down is harder because the water is resisting your movement. We can
imagine the movement of elementary particles being resisted by the Higgs fi eld, with
each particle interacting with the Higgs fi eld at a different strength. If the coupling
between the Higgs fi eld and the particle is strong, then the mass of the particle is large.
If it is weak, then the particle has a smaller mass. A particle like the photon with
zero rest mass doesn’t interact with the Higgs fi eld at all. If the Higgs fi eld didn’t
exist at all, then all particles would be massless. It is not certain what the mass of
the Higgs boson is, but current estimates place an upper limit of ≈140 GeV/c2.


希格斯玻色子（英语：Higgs boson）是标准模型预言存在的一种基本粒子，是一种玻色子，自旋为零，不带电荷、色荷，非常不稳定，在生成后会立刻衰变，于2013年3月14日暂时被确认存在。[1][2][7]:401-405这是一个重大的实验发现，对于希格斯场的存在与否也给出有力证据。[8]为什么某些基本粒子带有质量，而某些基本粒子的质量为零？根据希格斯机制，基本粒子是因为与遍布于宇宙的希格斯场耦合而获得质量。希格斯玻色子是希格斯场的振动，是希格斯场存在的明确证据，就好像从观察海面的波浪可以推论出大海的存在。[9][10][注 1]物理学者认为，倘若能够通过做实验更加了解希格斯玻色子的物理性质，这将会对粒子物理学造成极大的冲击，促使核对标准模型其它尚未经过检验的部分成为可能，指引粒子物理学的其它理论与发现，导致后标准模型物理（physics beyond the standard model）的研究与突破，[11]并且在这漫长过程中，发展出很多对于人类生活品质有所助益的崭新科技。[12][13]

希格斯玻色子是否存在？这是一个极为重要的基础物理问题。物理学者花费四十多年时间寻找它。至今为止，全世界最昂贵、最复杂的实验设施之一，大型强子对撞机（LHC），其建成的主要目的之一就是寻找与观察希格斯玻色子与其它种粒子。[14]2012年7月4日，欧洲核子研究组织（CERN）宣布，LHC的紧凑渺子线圈（CMS）探测到质量为125.3±0.6GeV的新玻色子（超过背景期望值4.9个标准差），超环面仪器（ATLAS）测量到质量为126.5GeV的新玻色子（5个标准差），这两种粒子极像希格斯玻色子。[15]2013年3月14日，欧洲核子研究组织发表新闻稿正式宣布，先前探测到的新粒子暂时确认是希格斯玻色子，具有零自旋与偶宇称，这是希格斯玻色子应该具有的两种基本性质，但有一部分实验结果不尽符合理论预测，更多数据仍旧等待处理与分析。[1][2]。

希格斯玻色子是因物理学者彼得·希格斯命名。[注 2]他是于1964年提出希格斯机制的六位物理学者中的一位。虽然这理论最终以希格斯的名字命名，在1960年至1972年之间，有很多物理学者对于这理论独立地做出不同贡献。2013年10月08日，因为“次原子粒子质量的生成机制理论，促进了人类对这方面的理解，并且最近由欧洲核子研究组织属下大型强子对撞机的超环面仪器及紧凑μ子线圈探测器发现的基本粒子证实”，弗朗索瓦·恩格勒、彼得·希格斯荣获2013年诺贝尔物理学奖。

http://zh.wikipedia.org/wiki/%E5%B8%8C%E6%A0%BC%E6%96%AF%E7%B2%92%E5%AD%90

http://zh.wikipedia.org/wiki/%E8%BF%B4%E5%9C%88%E9%87%8F%E5%AD%90%E9%87%8D%E5%8A%9B
圈量子引力论（loop quantum gravity，LQG），又译回圈量子重力论，英文别名圈引力（loop gravity）及量子几何学（quantum geometry）；由阿贝·阿希提卡（Ahbay Ashtekar）、李·施莫林（Lee Smolin）、卡洛·洛华利（Carlo Rovelli）等人发展出来的量子引力理论，与弦理论一并是目前为止将引力论量子化最成功的理论。

利用量子场论的微扰理论来实现引力论的量子化的理论是不能被重整化的。如果主张时空只有四维，从广义相对论下手，结果可以把广义相对论转变成类似规范场论的理论，基本正则变量为阿希提卡-巴贝罗联络（Ashtekar-Barbero Connection）而非度规张量,再以联络定义的平移算子（holonomy）以及通量变数(flux variable)为基本变量实现量子化。

在此理论下，时空描述是呈背景独立，由关系性循环织成的自旋网络铺成时空几何。网络中每条边及每个节点分别为一普朗克长度及普朗克体积。循环并不存在于时空中，循环扭结的方式定义时空几何。在普朗克尺度下，时空几何充满随机的量子涨落，因此自旋网络又称为自旋泡沫（Spin foam）。在此理论下，时空是离散的。

http://zh.wikipedia.org/wiki/%E9%87%8F%E5%AD%90%E5%BC%95%E5%8A%9B

量子引力，是对引力场进行量子化描述的理论，属于万有理论之一。研究方向主要尝试结合广义相对论与量子力学，为当前的物理学尚未解决的问题。当前主流尝试理论有：超弦理论、圈量子引力论、声学类比模型。


http://zh.wikipedia.org/wiki/M%E7%90%86%E8%AE%BA
M理论

在理论物理学中，M理论是弦理论的一种延展理论。M理论当中指出，描述完整的物理世界一共需要十一个维度，其维度超过弦理论所需要的十维，被支持者相信该理论统合了所有五种弦理论，并成为终极的物理理论。原始M理论的“M”字是取自于膜 （membrane），膜理论是一个统一化弦理论当中的建设性设计方案。不过，由于威腾比他的同行们更加怀疑膜理论的真确性，他最后选择了“M理论”而非“膜理论”作为理论名称。爱德华自此宣称M字的不同诠释方式，对于使用“M理论”的人们来说，是个可以采用涵义大有变化适用于个人品味的字，例如，Magic（魔术理论）、Mystery（神秘理论）及Mother theory（源母理论）等等。^[1] “M理论”的完整描述事实上并不存在，低熵动力学认为“M理论”当中的超引力是与二维膜及五维膜的相互作用的结果。这个构想是超对称理论在十一维当中的独特延伸，在设定的边界条件成立下，包含了低熵含量物质及相互作用完全确定下，由于新维度的出现导得“耦合常数”的增加，可推演出强耦合极限的IIA型弦理论。

建基于数量众多的弦理论学家的工作之上（包含了阿肖克·森、克里斯·赫尔、保罗·汤森、迈克尔·杜夫及约翰·席瓦兹），普林斯顿高等研究院的爱德华·威滕于1995年在南加州大学所举办的研讨会上提出了“M理论”，同时使用它解释了一批先前观察到的对偶性，启动了一波弦理论的研究热潮，在弦理论发展史当中被称为第二次超弦革命。

1990年代初，许多不同种类的超弦理论由对偶性建立起关连性，同一个对偶性物态可以在其他的超弦理论当中被描述为另外一种物态，这些关连性暗示每一种超弦理论都是一个更深层次理论的子集理论，这个理论由爱德华·威滕提出，并称之为“M理论”。

Supersymmetry
There exists yet another unifi cation scheme beyond that tackled by the GUTs. In
particle physics, there are two basic types of particles. These include the spin-1/2
matter particles (fermions) and the spin-1 force-carrying particles (bosons). In
elementary quantum mechanics, you no doubt learned that bosons and fermions
obey different statistics. While the Pauli exclusion principle prevents two fermions
from inhabiting the same state, there is no such limitation for bosons.
One might wonder why there are these two types of particles. In supersymmetry,
an attempt is made to apply the reasoning of Maxwell and propose that a symmetry
exists between bosons and fermions. For each fermion, supersymmetry proposes
that there is a boson with the same mass, and vice versa. The partners of the known
particles are called superpartners. Unfortunately, at this time there is no evidence
that this is the case. The fact that the superpartners do not have the same mass
indicates either that the symmetry of the theory is broken, in which case the masses
of the superpartners are much larger than expected, or that the theory is not correct
at all and supersymmetry does not exist.


Latter progress in theoretical particle physics prior to string theory came about in
the 1970s under the name of supersymmetry (SUSY). This is a symmetry that relates
or mixes (unites) fermions and bosons. Fermions are particles with half-integral
spin, while bosons are particles with integer spin. The idea of supersymmetry is that
for every fermion, there is a corresponding boson. We know that the force-carrying
or mediator bosons have spin-0 or spin-1, so what we would hope to fi nd is that
corresponding to spin-1/2 particles like quarks and electrons, there would be spin-0
or spin-1 particles (denoted the selectron and squark). Also, corresponding to each
spin-0 or spin-1 particle there would be a half-integral spin particle. The proposed
particles go by the fanciful names photino, wino, and gluino, which would
correspond to the photon, W, and gluon, for example.


Summary
Supersymmetry is a proposition to introduce a symmetry between fermions and
bosons. If such a symmetry exists, then there are supercharge operators that convert
fermion states into boson states and vice versa. In its most basic form, the theory
predicts that the partners of known particles, obtained by applying the supercharge
operators and known as superpartners, have the same mass. This has not been
experimentally observed. If supersymmetry is real, the masses of the superpartners
are much larger than the masses of known particles, and this explains why they
have not yet been detected experimentally. The difference in masses breaks the
supersymmetry. Hence we know supersymmetry is broken. Theorists have great hopes
for the theory because it solves many outstanding problems in theoretical physics, such
as the mass of the Higgs particle (the hierarchy problem). Supersymmetry may also
explain the existence of mysterious dark matter particles and it is of fundamental
importance to string theory.


The larger the symmetry of a physical system is, the more information
about the structure of the system can be obtained from the
mathematics of the relevant symmetry group.

得一万事毕，万界备全基。局域作投射，整体难见迹。
比喻万维事，类似张量积。万有探寻理，三才大统一。

The spatial dimensions not associated with the brane are called the bulk. The
volume of the brane is called the world-volume. Note that time fl ows everywhere,
in the bulk and on the D-brane as well.
A model of our universe has been proposed where we live in a D3-brane and the
bulk consists of the remaining extra spatial dimensions. Perhaps the most fundamental
physical insight that has resulted from the study of D-branes is that
• The interactions of the standard model (electromagnetism, strong, and
weak forces) are constrained to the brane.
• Gravity can escape from the brane. Gravitational forces are distributed in
the brane and also throughout the higher dimensions. Hence, the strength of
gravity is diluted by the higher dimensions. This explains why its strength
is so different from that of the other known forces.

Strings with endpoints on different branes acquire
mass from stretching of the string. Separating coincident D-branes provides a
mechanism through which the gauge fi elds can acquire mass.

What happens is the D-brane decays away into closed string states. Generally
speaking this is an artifact of bosonic string theory. In superstring theory there are
stable D-brane states. However, in superstring theory you can have an anti-D-brane,
which can be coincident with a D-brane. Like particles and antiparticles, they
annihilate. This is because there are tachyon states stretched between them.

The Laws of Black Hole Mechanics
In the early 1970s, James Bardeen, Brandon Carter, and Stephen Hawking found
that there are laws governing black hole mechanics which correspond very closely
to the laws of thermodynamics. The zeroth law states that the su***ce gravity κ at
the horizon of a stationary black hole is constant.
The fi rst law relates the mass m, horizon area A, angular momentum J, and charge
Q of a black hole as follows:
dm =(κ/8π) dA +Ω dJ +Φ dQ
This law is analogous to the law relating energy and entropy. We will see this more
precisely in a moment.
The second law of black hole mechanics tells us that the area of the event horizon
does not decrease with time. This is quantifi ed by writing:
dA ≥ 0
This is directly analogous to the second law of thermodynamics which tells us that
the entropy of a closed system is a nondecreasing function of time. A consequence
is that if black holes of areas A1 A2 and coalesce to form a new black
hole with area A3 then the following relationship must hold:
A3>= A1+ A2 
As you probably recall, an analogous relationship holds for entropy. Finally, we
arrive at the third law of black hole mechanics. This law states that it is impossible
to reduce the su***ce gravity κ to 0.
The correspondence between the laws of black hole mechanics and
thermodynamics is more than analogy. We can go so far as to say that the analogy
is taken to be real and exact. That is, the area of the horizon A is the entropy S of
the black hole and the su***ce gravity κ is proportional to the temperature of the
black hole. We can express the entropy of the black hole in terms of mass or area.
In terms of mass the entropy of a black holes is proportional to the mass of the black hole squared. In terms of area, the entropy is 1/4 of the area of the horizon in units
of Planck length:  
S=A/4LL

One of the recent successes of string theory has been its ability to count up the
microscopic states of a black hole to calculate its entropy. The result obtained in
this manner agrees with the semiclassical expressions, providing strong support for
string theory as a quantum theory of gravity.

The Holographic
Principle and AdS/CFT
Correspondence
In this chapter we will touch on one of the most interesting ideas to come out of the
study of quantum gravity and string theory in particular: the holographic principle.
This is an idea closely related to entropy, so we present it here after we have
completed our discussion of black holes and entropy in the last chapter. The
holographic principle appears to be a quite general feature of quantum gravity, but
we discuss it in the context of string theory. Our discussion largely follows that of
Susskind and Witten. Our focus will be on showing how the holographic principle
leads to an entropy bound of the type we found for black holes.

A Statement of the Holographic Principle
The holographic principle was fi rst proposed by Gerard t’Hooft in 1993 and has
been worked on extensively by Leonard Susskind. It can be asserted using two
postulates:
• The total information content in a volume of space is equivalent to a theory
that lives only on the su***ce area that encloses the region.
• The boundary of a region of space-time contains at most a single degree of
freedom per Planck area.
The holographic principle really applies to gravity and we have already seen it in
action when talking about black holes. Information content, which is another way
of saying entropy, is about counting the number of states in a system and so is
proportional to area. We have already seen that in the case of a black hole that
entropy is proportional to the area of the event horizon:
S=A/4G

where G is Newton’s gravitational constant. The area A is measured in Planck
units.
This is a surprising result because we would intuitively expect that the number of
states is proportional to the volume of the enclosed region. Following Susskind, we
illustrate that this is in fact the case when gravity is not involved. Imagine that a
volume V contains a set of spins on a lattice. We take the lattice spacing to be a, and
imagine that the lattice fi lls the entire volume. Then the total number of spins
contained in V is
# spins = V/aaa
The total number of states the system can have is
logN=(V/aaa)log2
Using thermodynamics, we arrive at a relationship between the number of states
and entropy S:
N ∝ expS
Hence we fi nd that S=(V/aaa)ln2
We’ve found what we intuitively expect—the entropy (and by extension the
amount of information) in the region is proportional to the volume. After all we
started off assuming we had a lattice of spins that fi lled the volume—so what else
could we get?
For black holes we found something very different. In that case, the entropy is
directly proportional to the area of the even horizon. So in some sense, gravity must
be different from other interactions. It turns out that the case of a black hole provides
the maximum entropy that a gravitational system can have.

AdS/CFT Correspondence
The framework of the holographic principle which comes out of string/M-theory is
known as AdS/CFT (anti-de Sitter/conformal fi eld theory) correspondence. We can
quantitatively describe the space-time using AdS space in fi ve dimensions. The
fi ve-dimensional AdS model has a boundary with four dimensions that looks like
fl at space with three spatial directions and one time dimension.
The AdS/CFT correspondence involves a duality, something we’re already
familiar with from our studies of superstring theories. This duality is between two
types of theories:
• Five-dimensional gravity
• Super Yang-Mills theory defi ned on the boundary
By “super” Yang-Mills theory we mean theory of particle interactions with
supersymmetry. The holographic principle comes out of the correspondence between
these two theories because Yang-Mills theory, which is happening on the boundary, is
equivalent to the gravitational physics happening in the fi ve-dimensional AdS geometry.
So the Yang-Mills theory can be colloquially thought of as a hologram on the boundary
of the real fi ve-dimensional space where the fi ve-dimensional gravitational physics is
taking place.


The Holographic Universe
http://www.crystalinks.com/holographic.html

String Theory and
Cosmology
Conventional cosmology, which grew out of general relativity, astrophysics, and
quantum fi eld theory, proposes that the universe began with a “big bang” at a fi nite
time in the past with an infl ationary rush, and will expand forever until the universe
dies with a whimper, as a result of increasing entropy eventually sapping the useful
life out of it. Proposals which originated in string/M-theory have led to different
cosmological models. These models have the unexpected and shocking ability to
describe the universe before the big bang. Based on a brane-world-type universe,
they involve the collision of two branes which get rid of the “singularity” of bigbang
theory and replace it with an eternal universe, which could be described as
“cyclic.” In this chapter, we give an overview of some of the cosmological models
that have arisen from string/M-theory. Unfortunately, the details of these models
using string/M-theory are well beyond the scope of this book, so our description
will be more of a qualitative nature. The motivated reader is urged to consult the
references for details. Cosmology is sure to be an active area of research in the
coming years with many new and possibly unexpected developments.

Brane Worlds and the Ekpyrotic Universe
A cosmological model based on M-theory was proposed by Neil Turok and Paul
Steinhardt.3 In the Randall-Sundrum model, we have a fi ve-dimensional universe
with two branes fi xed at the boundaries. Now imagine that instead the branes can
move along the fi fth dimension through the bulk. This idea is the origin of the ekpyrotic
universe, a model fully rooted in string/M-theory. In particular, the ekpyrotic scenario
is based on fi ve-dimensional heterotic M-theory. The models are studied with fi ve
space-time dimensions because we start with 11 space-time dimensions in M-theory,
and compactify six of the dimensions down to a tiny size which is irrelevant on
cosmological scales.
In this model, we are imagining a universe which has always existed, but which goes
through a cyclic pattern. This pattern begins with an initial state characterized by the
boundary branes living in a fl at, empty, and cold state. They are located at the boundaries
of the fi fth dimension and are parallel. As mentioned above, in the ekpyrotic scenario the
branes are moving, so they move toward one another and collide. The collision of the
branes, a process called ekpyrosis in the literature, is seen as the “big bang.” The energy
from the collision creates the matter in the brane. After collision, the branes move off
apart from one another and cool down. Eventually they return to the cold, empty, fl at
initial state, and the process begins all over again. The driving force behind this is a scalar
fi eld φ called the radion fi eld, which determines the distance between the branes. It
causes the universe to evolve through a period of slow acceleration, followed by
deceleration and contraction. It then triggers a bounce and reheating of the universe.

The scenario depicted here solves many cosmological riddles, if it is to be
believed. First let’s consider two major riddles solved by infl ation: homogeneity
and isotropy. Infl ation seeks to address this problem (explaining why the universe
is homogeneous and isotropic) by postulating the existence of a fi eld that turns on
for a brief instant causing the universe to expand exponentially. While this scenario
has been quantifi ed in a plausible manner, it is not unreasonable to have doubts
about a theory that describes a fi eld that turns on for a fl icker of an instant and turns
off as fast, never to be seen again in the entire history of the universe. So what does
the ekpyrotic scenario have to offer?
In the ekpyrotic scenario, there are two fl at, parallel branes that collide like two
nearly perfectly fl at metal plates, say. Since the branes are parallel they collide at
the same time (well almost anyway, let quantum theory intervene) at all points
along the branes. This action endows the visible brane with the same energy density
at all points with constant initial temperature called the ekpyrotic temperature. This
explains why the universe looks the same everywhere in all directions and why the
cosmic microwave background is the same everywhere—the universe began with
the same initial conditions at all points.
The fl atness problem is solved by setting the initial conditions of the branes to
the vacuum state. In the vacuum state the branes are fl at and empty, so no mysterious
fi ne tuning of matter density is required to make the universe turn out fl at. The
reasonable assumption that the branes start off in the vacuum state forces them to
be fl at.
Now, of course, quantum theory means that everything is not as exact as described
so far. Quantum fl uctuations in the branes called brane ripples result from the
movement of the branes along the fi fth dimension. These fl uctuations mean that not
every point on the brane collides with the other brane at exactly the same instant.
Instead, most will collide at some average time, while some will collide earlier than
average and some will collide later than average. Hence, rather than producing a
universe with an absolutely uniform temperature, the collision will produce a
universe with some regions slightly colder than average (because they collided
earlier) and some regions slightly hotter than average (because they collided later).
These are the seeds the universe needs to produce the large scale structures of the
universe like the galaxies. Once again, quantum effects are seen to give birth to
large scale cosmological structure, providing a link between the very large and the
very small in the universe.
One distasteful aspect of general relativity is the presence of “singularities” in
the theory. These are points in space-time where quantities like curvature (the
gravitational fi eld) and temperature blow up to infi nity. The “big-bang singularity”
is one such example.
In the ekpyrotic model, the singularity is far milder than in classical general
relativity. Two branes move toward each other, they collide, and then they bounce off
and return to their initial positions. The “big bang” is an event that occurs with a large but fi nite temperature. There is no singularity corresponding to infi nite
curvature. Matter and radiation densities on the branes are fi nite. And there is no
infi nitely small point where all of matter, space, and time supposedly sprung from
by magical fi at. However, there is singular behavior at the “big crunch” when the
two branes collide, because the extra dimension between them disappears during
the collision. After the branes separate and move off from each other the extra
dimension reappears. Of course, while this model dispenses with much of the
singular behavior of general relativity, it may be just as hard to believe that space
and time always existed. In the end, experiment and observation will be our guides
to determine in a scientifi c manner which scenario is closer to the truth.
The ekpyrotic scenario answers another mystery of cosmology, the origin of
matter. During the collision the kinetic energy of motion of the branes is converted
to heat or thermal energy. This is just like a car crash, where some of the energy of
motion of the cars is converted to heat. In the case of the branes, the heat energy can
be used to create matter via the Einstein relation E = mcc.
The current form of the ekpyrotic scenario is called the cyclic model of the
universe. It proposes that
• The big bang is not the origin of time.
• The universe always existed and runs through a repeated cycle of brane
collisions.
A cycle in the history of the universe goes as follows:
• Two branes collide providing a big bang which acts as a transition between
cycles. Matter and radiation are created.
• The hot big-bang phase creates large-scale structure in the universe.
• This is followed by a period of slow but accelerated expansion where the
universe cools down and dilutes.
The ekpyrotic scenario provides an alternative to infl ation that can be used to
explain many cosmological mysteries. Suprisingly, they may be able to be
distinguished by observational tests (at least in principle). Infl ation predicts that
gravitational waves are scale invariant. This is not the case for the ekpyrotic model.

Summary
We began exploring cosmological scenarios by considering the Kasner metric,
which allows some dimensions to contract while others expand as the universe
evolves. Models of this type are not satisfactory and so have been discarded. The
Randall-Sundrum model imagines the universe to be constructed out of two branes that bound a higher-dimensional bulk. This idea was extended in the ekpyrotic
model, which allows the branes to move and collide, explaining the big bang and
providing a string theory alternative to infl ation. The ekpyrotic scenario does not
say the big bang never happened, rather it explains the big bang without evoking a
singularity. Once the brane collision has occurred, the universe evolves according
to standard big-bang theory on the branes.

QFT

Field Quantization of Scalar Fields
We now turn to the task of quantizing a given fi eld ϕ(x). The process of quantization
which basically means creating a quantum theory from a classical one is based on
imposing commutation relations. Canonical quantization refers to the process of
imposing the fundamental commutation relation on the position and momentum
operators.
[xˆ, pˆ ] = i

In total, the quantization procedure is to
• Promote position and momentum functions to operators
• Impose the commutation relation Eq. (6.19)
We will follow a similar procedure for quantizing a classical fi eld theory. In this
case, the procedure is called second quantization.

SECOND QUANTIZATION
In quantum fi eld theory, we quantize the fi elds themselves rather than quantizing
dynamical variables like position. Once again we are faced with the problem of
having to put space and time on an equal footing. In nonrelativistic quantum
mechanics, position and momentum are operators. The position operator acts on a
wave function according to
Xˆψ (x) = xψ (x)
The momentum operator acts as
pˆ ψ(x) =-ih∂ψ (x)/∂x


On the other hand, time t is nothing but a parameter in nonrelativistic quantum
mechanics. Clearly it is treated differently than position, as there is no operator that
acts as
Tˆψ (x,t) = tψ (x,t)
Maybe you could try to construct a theory based on promoting time to such an
operator, but that is not what is done in quantum fi eld theory. What happens in
quantum fi eld theory is that we actually take the opposite approach, and demote
position and momentum from their lofty status as operators. In quantum fi eld theory,
time t and position x are just parameters that label a position in spacetime for a fi eld
as shown here.
ϕ(x,t)
To quantize the theory, we are going to take a different approach and treat the fi elds
themselves as operators. The procedure of second quantization is therefore to
• Promote the fi elds to operators, and
• Impose equal time commutation relations on the fi elds and their conjugate
momenta
Since we are quantizing the fi elds rather than the position and momentum, we call
this procedure second quantization—the type of quantization used in ordinary
quantum mechanics is fi rst quantization.

This is important so let’s summarize. In quantum fi eld theory,
• Position x and momentum p are not operators—they are just numbers like
in classical physics.
• The fi elds ϕ (x,t) and their conjugate momentum fi elds π (x,t) are
operators.
• Canonical commutation relations are imposed on the fi elds.
The fi elds are operators in the following sense. We have quantum states as we do
in quantum mechanics, but these are states of the fi eld. The fi eld operators act on
these states to destroy or create particles. This is important because in special
relativity,
• Particle number is not fi xed. Particles can be created and destroyed.
• To create a particle, we need at least twice the rest-mass energy E = mcc.
The mathematics that describe a quantum theory with changing particle number has
its roots in the simple harmonic oscillator, one of the few exactly solvable models.

The past decade has witnessed dramatic developments in the field of theoretical physics. This book is a comprehensive introduction to these recent developments. It contains a review of the Standard Model, covering non-perturbative topics, and a discussion of grand unified theories and magnetic monopoles. It introduces the basics of supersymmetry and its phenomenology, and includes dynamics, dynamical supersymmetry breaking, and electric-magnetic duality. The book then covers general relativity and the big bang theory, and the basic issues in inflationary cosmologies before discussing the spectra of known string theories and the features of their interactions. The book also includes brief introductions to technicolor, large extra dimensions, and the Randall-Sundrum theory of warped spaces. This will be of great interest to graduates and researchers in the fields of particle theory, string theory, astrophysics and cosmology. The book contains several problems, and password protected solutions will be available to lecturers at www.cambridge.org/9780521858410.

Michael Dine is Professor of Physics at the University of California, Santa
Cruz. He is an A. P. Sloan Foundation Fellow, a Fellow of the American Physical
Society, and a Guggenheim Fellow. Prior to this Professor Dine was a research
associate at the Stanford Linear Accelerator Center, a long-term member of the
institute for Advanced Study, and Henry Semat Professor at the City College of the
City University of New York.

“An excellent and timely introduction to a wide range of topics concerning
physics beyond the standard model, by one of the most dynamic
researchers in the field. Dine has a gift for explaining difficult concepts
in a transparent way. The book has wonderful insights to offer beginning
graduate students and experienced researchers alike.”
Nima Arkani-Hamed, Harvard University
“Howmany times did you need to find the answer to a basic question about
the formalism and especially the phenomenology of general relativity,
the Standard Model, its supersymmetric and grand unified extensions,
and other serious models of new physics, as well as the most important
experimental constraints and the realization of the key models within
string theory? Dine’s book will solve most of these problems for you and
give you much more, namely the state-of-the-art picture of reality as seen
by a leading superstring phenomenologist.”
Lubos Motl, Harvard University
“This book gives a broad overview of most of the current issues in theoretical
high energy physics. It introduces and discusses a wide range of
topics from a pragmatic point of view. Although some of these topics are
addressed in other books, this one gives a uniform and self-contained exposition
of all of them. The book can be used as an excellent text in various
advanced graduate courses. It is also an extremely useful reference book
for researchers in the field, both for graduate students and established
senior faculty. Dine’s deep insights and broad perspective make this book
an essential text. I am sure it will become a classic. Many physicists expect
that with the advent of the LHC a revival of model building will take
place. This book is the best tool kit a modern model builder will need.”
Nathan Seiberg, Institute for Advanced Study, Princeton

The Goldstone phenomenon

The appearance of massless particles when a symmetry is broken is known as
the Nambu–Goldstone phenomenon, and π is called a Nambu–Goldstone boson.
In any theory with scalars, a choice of minimum may break some symmetry. This
means that there is a manifold of vacuum states. The broken symmetry generators
are those which transform the system from one point on this manifold to another.
Because there is no energy cost associated with such a transformation, there is a
massless particle associated with each broken symmetry generator. This result is
very general. Symmetries can be broken not only by expectation values of scalar
fields, but by expectation values of composite operators, and the theorem holds.
A proof of this result is provided in Appendix B. In nature, there are a number of
excitations which can be identified as Goldstone or almost Goldstone (“pseudo-
Goldstone”) bosons. These include spin waves in solids and the pi mesons.We will
have much more to say about the pions later.



标准模型扩充[编辑]



[ltr]标准模型扩充 (***E) 是一个有效场论， 它包含了标准模型， 广义相对论和所有可以破坏洛仑兹对称的算符^{[1][2][3][4][5][6][7][8]}。 借助于这个一般的理论框架我们可以研究这种基本的对称性破缺。CPT对称破缺暗含洛伦兹对称破缺^[9]。 标准模型扩充包含了破坏和保持CPT对称的算符^[10][11][12]。

[/ltr]

1 发展

2 洛伦兹变换：观测者和粒子

3 ***E建模

4 自发性洛伦兹对称破缺

5 实验探索

6 参见

7 References

8 External links

[size][color][font][ltr]

发展[编辑]
Alan Kostelecký 和 Stuart Samuel在1989年证明了弦论中的相互作用可以导致自发洛仑兹对称破缺^[13]。 不久后的研究表明圈量子引力，非交换场论，膜宇宙学和随机动力学模型也同样包含了洛伦兹不变性的破缺^[14]。 由于一些关于量子引力的备选理论可以产生洛伦兹对称破缺，所以在过去的几十年里，涌现了大量关于洛伦兹对称破缺的研究。在二十世纪九十年代早期，研究表明在玻色子超弦理论中，弦相互作用也可以自发破缺CPT 对称，这预示着对于搜寻可能的CPT对称破缺信号，有着高精度的K介子干涉的相关实验将会大有前景^[15]。 ***E的提出是为了协助关于洛伦兹和CPT对称的实验研究，这给了我们研究这些对称破缺的理论动机。在1995年，有效相互作用作为最初的一步被提出^[16][17]。 尽管洛伦兹破缺的相互作用源于弦论等的构建，但是在低能情况下***E中产生的有效作用量却独立于以它为基础的理论。在这个有效理论中，每一项都包含着以它为基础的理论中的张量场的平均值。由于普朗克尺度的抑制，这些系数的量级都非常小，而且理论上都是实验可测的。由于中性介子的干涉性质使得他们对于抑制效应非常灵敏，最初的实验考虑了这些中性介子的混合。在1997和1998年，Don Colladay 和Alan Kostelecký在合作写的两篇文章里第一次提出了平直时空中的最小***E^[1][2]。这项工作对标准模型中的粒子的洛伦兹破缺提供了一个理论框架，也为潜在的新实验搜寻提供了关于信号类型的信息^{[18][19][20][21][22]}。
在2004年，Alan Kostelecký发表了弯曲时空中包含洛伦兹破缺的主要项^[3]， 完成了最小***E的构架。在1999年，Sidney Coleman 和 Sheldon Glashow提出了一个关于***E的各向同性极限^[23]。 关于高阶洛伦兹破缺项，它们在包括电动力学等各类理论中被广泛研究^[24]。
洛伦兹变换：观测者和粒子[编辑]
洛伦兹破缺表明在两个只相差一个粒子洛伦兹变换的系统中存在一个可测的差别。粒子和观测者洛伦兹破缺的差别对于理解物理学中的洛伦兹破缺十分重要。 在狭义相对论中，观测者洛伦兹变换把有着不同速度和方向的参考系中的测量联系起来。一个系统中的坐标和另一个系统中的坐标通过观测者洛伦兹变换联系起来-旋转，加速，或者两者的结合。由于这样的变换仅是坐标变换，对于处在两个不同参考系的观测者来说，物理定律是一样的。另一方面，同一观测者可以研究同一实验在旋转或者加速后的结果，这样的变换称为粒子变换，这是因为实验中的物质和场通过物理变换到了新的构形。
在惯用的真空中，观测者和粒子变换可以通过一种简单的方式联系起来-那就是其中一个是另一个的反变换。这种显然的等价通常被表述为主动和被动变换。但是，因为特定的背景场是对称破缺的来源，所以这种等价在包含洛伦兹破缺的理论中不成立。这些类似张量的背景场选择了特定的方向和依赖加速的效应。这些场存在于整个时空中，本质上是静态的。当对于其中某一个场灵敏的实验被旋转或者加速，也就是说，被进行了粒子变换，背景场仍然保持不变，这可能产生可观测的效应。由于坐标的变换不影响物理的本质，所以观测者洛伦兹变换对于包括与洛伦兹破缺有关的所有理论都成立。这种不变性在场论中通过表述成一个由相关时空指标缩并而成的标量拉格朗日密度来实现。当理论包含存在于整个宇宙中的特定***E背景场时，粒子洛伦兹破缺就产生了。
***E建模[编辑]
***E的拉格朗日密度由许多项构成，其中表示洛伦兹破缺的项是由标准场算符和控制洛伦兹破缺的系数缩并而成的观测标量。控制洛伦兹破缺的系数原则上可以由实验测定，因此这些系数并不是可以随意变化的参数。因为洛伦兹破缺是发生在普朗克尺度上的现象，所以这些系数应该非常小，我们可以用微扰理论来进行相当准确的计算。在有些情况下，其他原因会进一步限制洛伦兹破缺现象的观测。比如，迄今为止我们并未观测到与周围引力场有关的洛伦兹破缺现象，这可能是因为周围的引力场太弱的关系^[25]。一般而言，与其他相互作用相比，引力场中可能存在的洛伦兹破缺会更大一些。这一模型的稳定性和因果律也已经有了详细的研究^[26]。
自发性洛伦兹对称破缺[编辑]
场论中有两种实现对称破缺的方式：人为地设定显性对称破缺项和按动力学演化的系统自发性对称破缺。Alan Kostelecký在2004年发表了一个洛伦兹破缺的关键性结果，那就是显性洛伦兹破缺会导致Bianchi等式和能动量以及自旋密度张量的守恒定律不相容，然而自发性洛伦兹破缺并没有这一矛盾^[3]。这一结果要求所有的洛伦兹破缺现象都是有动力学演化的自发性破缺。正式的研究显示Nambu-Goldstone模式是可能的洛伦兹破缺机制。Nambu-Goldstone定理说明自发性对称破缺必然伴随着零质量玻色子的产生。这些玻色子模式可以是光子^[27]，引力子^[28][29]，自旋相互作用^[30] 以及非自旋相互作用^[25]。
实验探索[编辑]
***E模型能够计算给出实验中所有可能的洛伦兹破缺信号^{[31][32][33][34][35][36]}，因此它是实验领域里用来探索洛伦兹破缺的一个很好的工具。到现在为止，所有的实验结果都是以***E中控制洛伦兹破缺的系数的上限这一形式给出的。公布的结果所采用的参考系是日心系，其他惯性系中的实验结果也会转换成日心系中的数据来公布。这是因为日心系是实用而又精准的惯性参考系，可以在百年的时间单位上作为惯性系使用。 典型的实验是探索背景场和各种粒子特性的耦合，例如粒子的自旋，传播方向等。因为地球上的实验不可避免的相对于日心系有着转动，这就产生了一个洛伦兹破缺的关键信号。那就是所测得的洛伦兹破缺系数有随着周年的变化和随着恒星时的变化。由于地球绕太阳的转动是非相对论的，周年的变化一般会被减弱10⁻⁴。这就使得随恒星时的变化成为实验中主要搜索的洛伦兹破缺系数随时间的变化关系^[37]。
已有的涉及测量***E中洛伦兹破缺系数的实验包括：
[/ltr][/font][/color][/size]

• 宇宙源的双折射和色散
  
• 对钟实验
  
• 宇宙微波背景辐射的极化
  
• 碰撞实验
  
• 电磁共振腔
  
• 等价性原理
  
• 规范粒子以及希格斯粒子
  
• 高能天体物理观测
  
• 重力加速度测量
  
• 物质粒子干涉实验
  
• 中微子振荡
  
• K，B，D介子的振荡和衰变
  
• 粒子－反粒子对比
  
• 太阳系及其外的后牛顿引力学
  
• 第二代和第三代粒子
  
• 外太空任务
  
• 氢原子和反氢原子光谱
  
• 自选极化的物质粒子
  

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所有的***E系数实验结果都列在洛伦兹以及CPT破缺数据表里^[38]。
参见[编辑]
[/ltr][/font][/color][/size]

• 洛伦兹破缺的反物质测试
  
• 洛伦兹破缺的电动力学
  
• 洛伦兹破缺的中子振荡
  
• Bumblebee模型
  
• 狭义相对论检验
  
• 狭义相对论的检验理论
  

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References[编辑]
[/ltr][/font][/color][/size]

1. ^ ^1.0 1.1 D. Colladay and V.A. Kostelecký, CPT Violation and the Standard Model, Phys. Rev. D 55, 6760 (1997).
   
2. ^ ^2.0 2.1 D. Colladay and V.A. Kostelecký, Lorentz-Violating Extension of the Standard Model, Phys. Rev. D 58, 116002 (1998).
   
3. ^ ^{3.0 3.1 3.2} V.A. Kostelecký, Gravity, Lorentz Violation, and the Standard Model, Phys. Rev. D 69, 105009 (2004)
   
4. ^ Is Special Relativity Wrong? by Phil Schewe and Ben Stein, AIP Physics News Update Number 712 #1, December 13, 2004.
   
5. ^ Special Relativity Reconsidered by Adrian Cho, Science, Vol. 307. no. 5711, p. 866, 11 February 2005.
   
6. ^ Has time run out on Einstein's theory?, CNN, June 5, 2002.
   
7. ^ Was Einstein Wrong? Space Station Research May Find Out, JPL News, May 29, 2002.
   
8. ^ Peering Over Einstein's Shoulders by J.R. Minkel, Scientific American Magazine, June 24, 2002.
   
9. ^ O. Greenberg, CPT Violation Implies Violation of Lorentz Invariance, Phys. Rev. Lett. 89, 231602 (2002).
   
10. ^ Kostelecký, Alan. The Search for Relativity Violations. Scientific American Magazine.
    
11. ^ Russell, Neil. Fabric of the final frontier, New Scientist Magazine issue 2408, 16 August 2003.
    
12. ^ Time Slows When You're on the Fly by Elizabeth Quill, Science, November 13, 2007.
    
13. ^ V.A. Kostelecký and S. Samuel, Spontaneous Breaking of Lorentz Symmetry in String Theory, Phys. Rev. D 39, 683 (1989).
    
14. ^ Breaking Lorentz symmetry, Physics World, Mar 10, 2004.
    
15. ^ V.A. Kostelecký and R. Potting, CPT and strings, Nucl. Phys. B 359, 545 (1991).
    
16. ^ V.A. Kostelecký and R. Potting, CPT, Strings, and Meson Factories, Phys. Rev. D 51, 3923 (1995).
    
17. ^ IU Physicist offers foundation for uprooting a hallowed principle of physics, Indiana University News Room, January 5, 2009.
    
18. ^ New Ways Suggested to Probe Lorentz Violation, American Physical Society News, June 2008.
    
19. ^ Quantum gravity: Back to the future, Nature 427, 482-484 (5 February 2004).
    
20. ^ Lorentz Violations? Not Yet by Phil Schewe, James Riordon, and Ben Stein, Number 623 #2, February 5, 2003.
    
21. ^ Relativity: Testing times in space, Nature 416, 803-804, (25 April 2002).
    
22. ^ Catching relativity violations with atoms by Quentin G. Bailey, APS Viewpoint, Physics 2, 58 (2009).
    
23. ^ S. Coleman and S.L. Glashow, High-energy tests of Lorentz invariance, Phys. Rev. D 59, 116008 (1999).
    
24. ^ V.A. Kostelecký and M. Mewes, Electrodynamics with Lorentz-Violating Operators of Arbitrary Dimension, Phys. Rev. D 80, 015020 (2009).
    
25. ^ ^25.0 25.1 V.A. Kostelecký and J. Tasson, Prospects for Large Relativity Violations in Matter-Gravity Couplings, Phys. Rev. Lett. 102, 010402 (2009).
    
26. ^ V.A. Kostelecký and R. Lehnert, Stability, Causality, and Lorentz and CPT Violation, Phys. Rev. D 63, 065008 (2001).
    
27. ^ R. Bluhm and V.A. Kostelecký, Spontaneous Lorentz Violation, Nambu-Goldstone Modes, and Gravity, Phys. Rev. D 71, 065008 (2005).
    
28. ^ V.A. Kostelecký and R. Potting, Gravity from Spontaneous Lorentz Violation, Phys. Rev. D 79, 065018 (2009).
    
29. ^ V.A. Kostelecký and R. Potting, Gravity from Local Lorentz Violation, Gen. Rel. Grav. 37, 1675 (2005).
    
30. ^ N. Arkani-Hamed, H.C. Cheng, M. Luty, and J. Thaler, Universal dynamics of spontaneous Lorentz violation and a new spin-dependent inverse-square law force, JHEP 0507, 029 (2005).
    
31. ^ Unification could be ripe for the picking, Physics World, Jan 13, 2009.
    
32. ^ Michelson–Morley experiment is best yet by Hamish Johnston, Physics World, Sep 14, 2009.
    
33. ^ Neutrinos: The key to a theory of everything by Marcus Chown, New Scientist Magazine issue 2615, 1 August 2007.
    
34. ^ Einstein's relativity survives neutrino test, Indiana University News Room, October 15, 2008.
    
35. ^ Relativity violations may make light by Francis Reddy, Astronomy Magazine, June 21, 2005.
    
36. ^ Antimatter and matter may have different properties, Indiana University News Room.
    
37. ^ Lorentz symmetry stays intact, Physics World, Feb 25, 2003.
    
38. ^ V.A. Kostelecký and N. Russell, Data Tables for Lorentz and CPT Violation, Rev. Mod. Phys. (2011)
    

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External links[编辑]
[/ltr][/font][/color][/size]

• Background information on Lorentz and CPT violation
  
• Data Tables for Lorentz and CPT Violation
  

This phenomenon, that the gauge boson becomes massive when the gauge symmetry
is spontaneously broken, is known as the Higgs mechanism. While formally
quite similar to the Goldstone phenomenon, it is also quite different. The fact that
there is no massless particle associated with motion along the manifold of ground
states is not surprising – these states are all physically equivalent. Symmetry breaking,
in fact, is a puzzling notion in gauge theories, since gauge transformations
describe entirely equivalent physics (gauge symmetry is often referred to as a redundancy
in the description of a system). Perhaps the most important lesson here
is that gauge invariance does not necessarily mean, as it does in electrodynamics,
that the gauge bosons are massless.

Goldstone and Higgs phenomena for non-Abelian symmetries
Both the Goldstone and Higgs phenomena generalize to non-Abelian symmetries.
In the case of global symmetries, for every generator of a broken global symmetry,
there is a massless particle. For local symmetries, each broken generator gives rise
to a massive gauge boson.


Confinement
There is still another possible realization of gauge symmetry: confinement. This
is crucial to our understanding of the strong interactions. As we will see, Yang–
Mills theories, without too much matter, become weak at short distances. They
become strong at large distances. This is just what is required to understand the
qualitative features of the strong interactions: free quark and gluon behavior at very
large momentum transfers, but strong forces at larger distances, so that there are no
free quarks or gluons. As is the case in the Higgs mechanism, there are no massless
particles in the spectrum of hadrons: QCD is said to have a “mass gap.” These
features of strong interactions are supported by extensive numerical calculations,
but they are hard to understand through simple analytic or qualitative arguments
(indeed, if you can offer such an argument, you can win one of the Clay prizes of
$1 million).We will have more to say about the phenomenon of confinement when
we discuss lattice gauge theories.
One might wonder: what is the difference between the Higgs mechanism and
confinement? This questionwas first raised by Fradkin and Shenker and by ’t Hooft,
who also gave an answer: there is often no qualitative difference. The qualitative
features of a Higgs theory like the weak interactions can be reproduced by a confined,
strongly interacting theory. However, the detailed predictions of the weakly
interacting Weinberg–Salaam theory are in close agreement with experiment, and
those of the strongly interacting theory are not.


The quantization of Yang–Mills theories
In this book, we will encounter a number of interesting classical phenomena in
Yang–Mills theory but, in most of the situations in nature which concern us, we
are interested in the quantum behavior of the weak and strong interactions. Abelian
theories such as QED are already challenging. One can perform canonical quantization
in a gauge, such as Coulomb gauge or a light cone gauge, in which unitarity
is manifest – all of the states have positive norm. But in such a gauge, the covariance
of the theory is hard to see. Or one can choose a gauge where Lorentz invariance
is manifest, but not unitarity. In QED it is not too difficult to show at the level of
Feynman diagrams that these gauge choices are equivalent. In non-Abelian theories,
canonical quantization is still more challenging. Path integral methods provide
a much more powerful approach to the quantization of these theories.

弱相互作用[编辑]

粒子物理学标准模型

标准模型 [th] ]显示] 背景[/th][th] ]显示] 组成[/th][th] ]显示] 限制[/th][th] ]显示] 理论家[/th]

查   论   编

[ltr]
弱相互作用（又称弱力或弱核力）是自然的四种基本力中的一种，其余三种为强核力、电磁力及万有引力。次原子粒子的放射性衰变就是由它引起的，恒星中一种叫氢聚变的过程也是由它启动的。弱相互作用会影响所有费米子，即所有自旋为半奇数的粒子。
在粒子物理学的标准模型中，弱相互作用的理论指出，它是由W及Z玻色子的交换（即发射及吸收）所引起的，由于弱力是由玻色子的发射（或吸收）所造成的，所以它是一种非接触力。这种发射中最有名的是β衰变，它是放射性的一种表现。重的粒子性质不稳定，由于Z及W玻色子比质子或中子重得多，所以弱相互作用的作用距离非常短。这种相互作用叫做“弱”，是因为它的一般强度，比电磁及强核力弱好几个数量级。大部份粒子在一段时间后，都会通过弱相互作用衰变。弱相互作用有一种独一无二的特性——那就是夸克味变——其他相互作用做不到这一点。另外，它还会破坏宇称对称及CP对称。夸克的味变使得夸克能够在六种“味”之间互换。
弱力最早的描述是在1930年代，是四费米子接触相互作用的费米理论：接触指的是没有作用距离（即完全靠物理接触）。但是现在最好是用有作用距离的场来描述它，尽管那个距离很短。在1968年，电磁与弱相互作用统一了，它们是同一种力的两个方面，现在叫电弱力。
弱相互作用在粒子的β衰变中最为明显，在由氢生产重氢和氦的过程中（恒星热核反应的能量来源）也很明显。放射性碳定年法用的就是这样的衰变，此时碳-14通过弱相互作用衰变成氮-14。它也可以造出辐射冷光，常见于超重氢照明；也造就了β伏这一应用领域（把β射线的电子当电流用）^[1]。[/ltr]

• 1 性质
  
  
  
  • 1.1 弱同位旋与弱超荷
    
  • 1.2 对称破缺
    
  
  
  
• 2 相互作用类型
  
  
  
  • 2.1 载荷流相互作用
    
  • 2.2 中性流相互作用
    
  
  
  
• 3 电弱理论
  
• 4 参考资料
  
  
  
  • 4.1 大众书籍
    
  • 4.2 科学书籍
    
  • 4.3 注释
    
  
  
  

[ltr]

性质[编辑][/ltr]


[ltr]
弱相互作用有如下的数项特点：[/ltr]

1. 唯一能够改变夸克味的相互作用。
   
2. 唯一能令宇称不守恒的相互作用。因此它也是唯一违反CP对称的相互作用。
   
3. 由具质量的规范玻色子所介导的相互作用。这一不寻常的特点可由标准模型的希格斯机制得出。
   

[ltr]
由于弱相互作用载体粒子（W及Z玻色子）质量很大（约 90 GeV/c^2[2]），所以他们的寿命很短：平均寿命约为 3 × 10^-25秒^[3]。弱相互作用的耦合常数（相互作用强度的一个指标）介乎10⁻⁷与10⁻⁶之间，而相比下，强相互作用的耦合常数约为1^[4]，故就强度而言，弱相互作用是弱的^[5]。弱相用作用的作用距离很短（约为10⁻¹⁷–10⁻¹⁶ m^[5]）^[4]。在大约10⁻¹⁸米的距离下，弱相互作用的强度与电磁大约一致；但在大约3×10⁻¹⁷的距离下，弱相互作用比电磁弱一万倍^[6]。
在标准模型中，弱相互作用会影响所有费米子，还有希格斯玻色子；弱相互作用是除引力相互作用外唯一一种对中微子有效的相互作用^[5]。弱相互作用并不产生束缚态（它也不需要束缚能）——引力在天文距离下这样做，电磁力在原子距离下这样做，而强核力则在原子核中这样做^[7]。
它最明显的过程是由第一项特点所造成的：味变。比方说，一个中子比一个质子（中子的核子拍档）重，但它不能在没有变味（种类）的情况下衰变成质子，它两个“下夸克”中的一个需要变成“上夸克”。由于强相互作用和电磁相互作用都不允许味变，所以它一定要用弱相互作用；没有弱相互作用的话：夸克的特性，如奇异及魅（与同名的夸克相关），会在所有相互作用下守恒。因为弱衰变的关系，所以所有介子都不稳定^[8]。在β衰变这个过程下，中子里面的“下夸克”，会发射出一个虚W−
玻色子，它随即衰变成一电子及一反电中微子^[9]。
由于玻色子的大质量，所以弱衰变相对于强或电磁衰变，可能性是比较低的，因此发生得比较慢。例如，一个中性π介子在通过电磁衰变时，寿命约为10^-16秒；而一个带电π介子的通过弱核力衰变时，寿命约为10^-8秒，是前者的一亿倍^[10]。相比下，一个自由中子（通过弱相互作用衰变）的寿命约为15分钟^[9]。[/ltr]