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内容简介
The Standard Model has reigned triumphant for three decades. For just as long,theorists and experimentalists have speculated about what might lie beyond. Manyof these speculations point to a particular energy scale, the teraelectronvolt (TeV)scale which will be probed for the first time at the LHC. The stimulus for thesestudies arises from the most mysterious - and still missing - piece of the StandardModel: the Higgs boson. Precision electroweak measurements strongly suggest thatthis particle is elementary (in that any structure is likely far smaller than its Comptonwavelength), and that it should be in a mass range where it will be discovered at theLHC. But the existence of fundamental scalars is puzzling in quantum field theory,and strongly suggests new physics at the TeV scale. Among the most prominentproposals for this physics is a hypothetical new symmetry of nature, supersymmetry,which is the focus of much of this text. Others, such as technicolor, and large orwarped extra dimensions, are also treated here.
内页插图
目录
Preface
A note on choice ofmetric
Text website
Part 1 Effective field theory:the Standard Model,supersymmetry,unification
1 Before the Standard Model
Suggested reading
2 The Standard Model
2.1 Yan9—Mills theory
2.2 Realizations of symmetry in quantum field theory
2.3 The quantization of Yan9—Mills theories
2.4 The particles and fields of the Standard Model
2.5 The gauge boson masses
2.6 Quark and lepton masses
Suggested reading
Exercises
3 Phenomenology of the Standard Model
3.1 The weak interactions
3.2The quark and lepton mass matrices
3.3 The strong interactions
3.4The renormalization group
3.5 Calculating the beta function
3.6The strong interactions and dimensional transmutation
3.7 Confinement and lattice gauge theory
3.8 Strong interaction processes at high momentum transfer.
Suggested reading
Exercises
4 The Standard Model as an effective field theory
4.1Lepton and baryon number violation’
4.2 Challenges for the Standard Model
4.3 The hierarchy problem
4.4Dark matter and dark energy
4.5 Summary:successes and limitations of the
Standard Model
Suggested reading
5 Anomalies,instantons and the strong CP problem
5.1 The chiral anomaly
5.2 A two-dimensional detour
5.3 Real QCD
5.4 The strong CP problem
5.5 Possible solutions of the strong CP problem
Suggested reading
Exercises
6 Grand unification
6.1 Cancellation of anomalies
6.2 Renormalization of couplings
6.3 Breaking to SU(3)×SU(2)×U(1)
6.4 SU(2)×U(1)breaking
6.5 Charge quantization and magnetic monopoles
6.6Proton decay
6.7 Other groups
Suggested reading
Exercises
7 Magnetic monopoles and solitons
7.1 Solitons in 1+1 dimensions
7.2 Solitons in 2+1 dimensions:strings or vortices
7.3 Magnetic monopoles
7.4 The BPS limit’
7.5 Collective coordinates for the monopole solution
7.6 The Witten effect:the electric charge in the presence of θ
7.7 Electric—magnetic duality
Suggested reading
Exercises
8 Technicolor:a first attempt to explain hierarchies
8.1 QCD in a world without Higgs fields
8.2 Fermion masses:extended technicolor
8.3 Precision electroweak measurements
Suggested reading
Exercises
Part 2 Supersymmetry
9 Supersymmetry
9.1 The supersymmetry algebra and its representations
9.2 Superspace
9.3 N —— 1 Lagrangians
9.4 The supersymmetry currents
9.5 The ground-state energy in globally supersymmetric theories
9.6 Some simple models
9.7 Non-renormalization theorems
9.8 Local supersymmetry: supergravity
Suggested reading
Exercises
10 A first look at supersymmetry breaking
10.1Spontaneous supersymmetry breaking
10.2The goldstino theorem
10.3Loop corrections and the vacuum degeneracy
10.4Explicit, soft supersymmetry breaking
10.5Supersymmetry breaking in supergravity models
Suggested reading
Exercises
11 The Minimal Supersymmetric Standard Model
11.1Soft supersymmetry breaking in the MSSM
11.2SU(2)U(I) breaking
11.3Why is one Higgs mass negative?
11.4Radiative corrections to the Higgs mass limit
11.5Embedding the MSSM in supergravity
11.6The#term
11.7Constraints on soft breakings
Suggested reading
Exercises
12 Supersymmetric grand unification
12.1A supersymmetric grand unified model
12.2Coupling constant unification
12.3Dimension-five operators and proton decay
Suggested reading
Exercises
13 Supersymmetric dynamics
13. l Criteria for supersymmetry breaking: the Witten index
13.2 Gaugino condensation in pure gauge theories
13.3 Supersymmetric QCD
13.4 Nf < N: anon-perturbative superpotential
13.5 The superpotential in the case Nf < N - 1
13.6 Nf = N - 1 : the instanton-generated superpotential
Suggested reading
Exercises
14 Dynamical supersymmetry breaking
14.1 Models of dynamical supersymmetry breaking
14.2 Particle physics and dynamical supersymmetry breaking
Suggested reading
Exercises
15 Theories with more than four conserved supercharges
15.1 N = 2 theories: exact moduli spaces
15.2 A still simpler theory: N ———— 4 Yang-Mills
15.3 A deeper understanding of the BPS condition
15.4 Seiberg-Witten theory
Suggested reading
Exercises
16 More supersymmetric dynamics
16.1 Conformaily invariant field theories
16.2 More supersymmetric QCD
16.3 Nf = Ne
16.4 Nf>N+I
16.5 Nf > 3/2N
Suggested reading
Exercises
17 An introduction to general relativity
17.1 Tensors in general relativity
17.2 Curvature
17.3 The gravitational action
17.4 The Schwarzschild solution
17.5 Features of the Schwarzschiid metric
17.6 Coupling spin0rs to gravity
Suggested reading
Exercises
18 Cosmology
18.1 A history of the universe
……
Part 3 String theory
Part 4 The appendices
References
Index
精彩书摘
The strong interactions, as their name implies, are characterized by strong cou-pling. As a result, perturbative methods are not suitable for most questions. Incomparing theory and experiment, it is necessary to focus on a few phenomenawhich are accessible to theoretical analysis. By itself, this is not particularly dis-turbing. A parallel with the quantum mechanics of electrons interacting with nucleiis perhaps helpful. We can understand simple atoms in detail; atoms with verylarge Z can be treated by Hartree-Fock or other methods. But atoms with inter-mediate Z can be dealt with, at best, by detailed numerical analysis accompaniedby educated guesswork. Molecules are even more problematic, not to mentionsolids. But we are able to make detailed tests of the theory (and its extensionin quantum electrodynamics) from the simpler systems, and develop qualitativeunderstanding of the more complicated systems. In many cases, we can do quanti-tative analysis of the small fluctuations about the ground states of the complicatedsystem.
In the theory of strong interactions, as we will see, many problems are hopelesslycomplicated. Low-lying spectra are hard; detailed exclusive cross sections in high-energy scattering essentially impossible. But there are many que~stions we cananswer. Rates for many inclusive questions at very high energy and momentumtransfer can be calculated with high precision. Qualitative features of the low lyingspectrum of hadrons and their interactions at low energies can be understood in aqualitative (and sometimes quantitative) fashion by symmetry arguments. Recently,progress in lattice gauge theory has made it possible to perform calculations whichpreviously seemed impossible, for features of spectra and even for interaction ratesimportant for understanding the weak interactions.
前言/序言
As this is being written, particle physics stands on the threshold of a new era, withthe commissioning of the Large Hadron Collider (LHC) not even two years away.In writing this book, I hope to help prepare graduate students and postdoctoralresearchers for what will hopefully be a period rich in new data and surprisingphenomena.
The Standard Model has reigned triumphant for three decades. For just as long,theorists and experimentalists have speculated about what might lie beyond. Manyof these speculations point to a particular energy scale, the teraelectronvolt (TeV)scale which will be probed for the first time at the LHC. The stimulus for thesestudies arises from the most mysterious - and still missing - piece of the StandardModel: the Higgs boson. Precision electroweak measurements strongly suggest thatthis particle is elementary (in that any structure is likely far smaller than its Comptonwavelength), and that it should be in a mass range where it will be discovered at theLHC. But the existence of fundamental scalars is puzzling in quantum field theory,and strongly suggests new physics at the TeV scale. Among the most prominentproposals for this physics is a hypothetical new symmetry of nature, supersymmetry,which is the focus of much of this text. Others, such as technicolor, and large orwarped extra dimensions, are also treated here. Even as they await evidence for such new phenomena, physicists have becomemore ambitious, attacking fundamental problems of quantum gravity, and specu-lating on possible final formulations of the laws of nature. This ambition has beenfueled by string theol., which seems to provide a complete framework for thequantum mechanics of gauge theory and gravity. Such a structure is necessary togive a framework to many speculations about beyond the Standard Model physics.Most models of supersymmetry breaking, theories of large extra dimensions, andwarped spaces cannot be discussed in a consistent way otherwise.
宇宙的宏伟叙事:从经典力学到量子信息的前沿探索 本书旨在为物理学、数学及相关领域的研究者和高级学生提供一个全面而深入的视角,探讨自经典物理学的基石建立以来,人类对自然界基本规律理解的演进,并重点聚焦于现代物理学最前沿的几个交叉领域——量子场论的构造、广义相对论的几何解释,以及信息论在物理学中的应用。我们致力于构建一个清晰的知识框架,追踪理论物理学在过去一个世纪中如何从描述宏观现象转向探究微观粒子与时空本质的深刻联系。 第一部分:经典基石与黎曼几何的回归 本部分将首先回顾经典物理学的成就,这些成就构成了理解现代物理的逻辑起点。 第一章:牛顿力学的精炼与拉格朗日-哈密顿形式的统一 我们将从牛顿运动定律出发,迅速过渡到更具普适性的变分原理。重点分析拉格朗日力学如何通过能量泛函(Lagrangian)优雅地描述多粒子系统的动力学,强调其对坐标变换的不变性(诺特定理的先导)。随后,深入探讨哈密顿力学的框架,解析相空间的概念以及正则变换的数学结构。理解哈密顿力学不仅是理解经典混沌的工具,更是量子力学基本正则对易关系的直接思想来源。 第二章:场论的萌芽与电磁学的几何视角 电磁场理论是物理学中第一个成功的“场”的理论。本章将详细梳理麦克斯韦方程组,分析其洛伦兹协变性。我们将超越单纯的场方程求解,转而关注电磁学的规范不变性。通过引入规范势(Gauge Potential)的概念,为后续量子场论中基本力的描述奠定几何和拓扑的基础。 第三章:广义相对论的几何化——时空的新理解 爱因斯坦的广义相对论是经典物理学的巅峰,它将引力视为时空本身的弯曲。本章的重点在于黎曼几何的应用。我们将详细介绍: 1. 张量分析基础:协变导数、里奇张量和黎曼曲率张量,理解度规张量(Metric Tensor)如何编码时空的几何结构。 2. 爱因斯坦场方程的推导与物理解释:分析引力如何由物质和能量(应力-能量张量)决定,以及时空的演化如何反过来约束物质的运动。 3. 经典解的探索:简要回顾史瓦西解(黑洞的几何描述)和弗里德曼-勒梅特-罗伯逊-沃尔克(FLRW)度规在宇宙学中的应用,强调曲率在决定宇宙命运中的核心作用。 第二部分:迈向微观:量子力学的深度解析 本部分将严格地审视量子力学的基本公设,并将其提升到算符代数的层面。 第四章:量子力学的数学结构与希尔伯特空间 我们从薛定谔绘景过渡到狄拉克绘景。重点是: 1. 状态空间:理解可分离希尔伯特空间作为系统的状态空间,以及态矢量(ket vectors)的物理意义。 2. 可观测量的表象:自伴随算符(Hermitian Operators)如何对应于物理可观测量的本征值。 3. 演化方程:哈密顿算符在时间演化中的作用,以及幺正变换保证了概率守恒的原理。 第五章:角动量理论与自旋的内在性 角动量是量子系统中最基本的守恒量之一。本章将深入探讨: 1. 对易关系与本征值问题:详细求解 $L^2$ 和 $L_z$ 的本征值,理解球面谐波函数。 2. 自旋的引入:区别于轨道角动量,自旋是粒子内在的、不可约的自由度。通过泡利矩阵(Pauli Matrices)及其代数结构,展示非对易性如何从根本上改变了粒子的统计性质。 第三部分:从量子场到规范理论:现代物理学的语言 本部分是全书的核心,它构建了粒子物理学标准模型(Standard Model)的数学框架。 第六章:经典场论到量子场论的跃迁 量子力学将粒子视为概率波包,而量子场论(QFT)则将粒子视为场的量子激发。 1. 二次量子化:通过将经典场量提升为算符,引入产生(Creation)和湮灭(Annihilation)算符。 2. 真空态与粒子定义:精确定义真空态,并展示这些算符如何构建多粒子态。 3. 相对论性量子场论的挑战:引入Klein-Gordon方程和Dirac方程,分析自由场论的构建过程,并初步讨论因果性问题。 第七章:相互作用与微扰论——费曼图的诞生 真实的物理世界充满了相互作用。本章将聚焦于如何量化这些相互作用: 1. 相互作用绘景与S矩阵:定义散射过程的概率幅,即S矩阵。 2. Dyson级数展开:利用微扰论将S矩阵展开,展示其系统性的结构。 3. 费曼规则的建立:通过将Dyson级数的每一项与特定的费曼图对应起来,将抽象的积分运算转化为一套清晰的图形化规则,这是计算高阶过程的基石。 第八章:规范场论的普适性 规范对称性是描述基本相互作用力的核心原则。 1. 从Abelian到Non-Abelian规范群:从电磁学的U(1)规范群(电弱理论的前身)推广到SU(2)和SU(3)等非阿贝尔群。 2. 规范场与规范玻色子:解释如何通过要求场论对局域规范变换保持不变性,从而唯一地确定出传递相互作用的玻色子(如光子、胶子)。 3. 重整化基础:简要介绍紫外发散问题的出现,以及重整化程序——物理学中最成功的“修补”技术——如何使理论在有限能量尺度内具有预测能力。 第四部分:时空与信息的交织 本部分探讨理论物理学中新兴的、跨学科的领域,它们正在重新定义我们对信息、引力和量子力学的理解。 第九章:几何与拓扑的现代应用 本章将视野从四维时空扩展到更高维空间,并关注拓扑结构在物理学中的作用: 1. 拓扑绝缘体:利用拓扑不变量(如陈数)来描述材料的能带结构,解释为何边缘态具有鲁棒的保护性。 2. 霍尔效应的量子化:从拓扑角度理解朗道能级与量子霍尔效应的精确量化。 第十章:信息论与量子计算的前沿 现代物理学日益关注信息在物理系统中的角色。 1. 量子信息基础:介绍量子比特(Qubit)、量子纠缠(Entanglement)的概念,并讨论冯·诺依曼熵与纠缠熵的区别。 2. 黑洞热力学与信息悖论:回顾Bekenstein对黑洞熵的奠基性工作,并分析霍金辐射带来的信息丢失问题,探讨其对时空局部性的冲击。 3. 信息与引力的联系:讨论AdS/CFT对偶的概念,它暗示了引力理论可能(在某些背景下)可以从一个低一维的、纯粹的量子场论中“涌现”出来,突显信息如何可能成为时空结构的基本要素。 本书旨在通过这种结构化的、由浅入深的论述,引导读者构建起一个坚实的理论物理学知识体系,使其能够理解和参与到当代物理学中最激动人心的探索之中。