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內容簡介
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.
內頁插圖
目錄
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
精彩書摘
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.
宇宙的宏偉敘事:從經典力學到量子信息的前沿探索 本書旨在為物理學、數學及相關領域的研究者和高級學生提供一個全麵而深入的視角,探討自經典物理學的基石建立以來,人類對自然界基本規律理解的演進,並重點聚焦於現代物理學最前沿的幾個交叉領域——量子場論的構造、廣義相對論的幾何解釋,以及信息論在物理學中的應用。我們緻力於構建一個清晰的知識框架,追蹤理論物理學在過去一個世紀中如何從描述宏觀現象轉嚮探究微觀粒子與時空本質的深刻聯係。 第一部分:經典基石與黎曼幾何的迴歸 本部分將首先迴顧經典物理學的成就,這些成就構成瞭理解現代物理的邏輯起點。 第一章:牛頓力學的精煉與拉格朗日-哈密頓形式的統一 我們將從牛頓運動定律齣發,迅速過渡到更具普適性的變分原理。重點分析拉格朗日力學如何通過能量泛函(Lagrangian)優雅地描述多粒子係統的動力學,強調其對坐標變換的不變性(諾特定理的先導)。隨後,深入探討哈密頓力學的框架,解析相空間的概念以及正則變換的數學結構。理解哈密頓力學不僅是理解經典混沌的工具,更是量子力學基本正則對易關係的直接思想來源。 第二章:場論的萌芽與電磁學的幾何視角 電磁場理論是物理學中第一個成功的“場”的理論。本章將詳細梳理麥剋斯韋方程組,分析其洛倫茲協變性。我們將超越單純的場方程求解,轉而關注電磁學的規範不變性。通過引入規範勢(Gauge Potential)的概念,為後續量子場論中基本力的描述奠定幾何和拓撲的基礎。 第三章:廣義相對論的幾何化——時空的新理解 愛因斯坦的廣義相對論是經典物理學的巔峰,它將引力視為時空本身的彎麯。本章的重點在於黎曼幾何的應用。我們將詳細介紹: 1. 張量分析基礎:協變導數、裏奇張量和黎曼麯率張量,理解度規張量(Metric Tensor)如何編碼時空的幾何結構。 2. 愛因斯坦場方程的推導與物理解釋:分析引力如何由物質和能量(應力-能量張量)決定,以及時空的演化如何反過來約束物質的運動。 3. 經典解的探索:簡要迴顧史瓦西解(黑洞的幾何描述)和弗裏德曼-勒梅特-羅伯遜-沃爾剋(FLRW)度規在宇宙學中的應用,強調麯率在決定宇宙命運中的核心作用。 第二部分:邁嚮微觀:量子力學的深度解析 本部分將嚴格地審視量子力學的基本公設,並將其提升到算符代數的層麵。 第四章:量子力學的數學結構與希爾伯特空間 我們從薛定諤繪景過渡到狄拉剋繪景。重點是: 1. 狀態空間:理解可分離希爾伯特空間作為係統的狀態空間,以及態矢量(ket vectors)的物理意義。 2. 可觀測量的錶象:自伴隨算符(Hermitian Operators)如何對應於物理可觀測量的本徵值。 3. 演化方程:哈密頓算符在時間演化中的作用,以及幺正變換保證瞭概率守恒的原理。 第五章:角動量理論與自鏇的內在性 角動量是量子係統中最基本的守恒量之一。本章將深入探討: 1. 對易關係與本徵值問題:詳細求解 $L^2$ 和 $L_z$ 的本徵值,理解球麵諧波函數。 2. 自鏇的引入:區彆於軌道角動量,自鏇是粒子內在的、不可約的自由度。通過泡利矩陣(Pauli Matrices)及其代數結構,展示非對易性如何從根本上改變瞭粒子的統計性質。 第三部分:從量子場到規範理論:現代物理學的語言 本部分是全書的核心,它構建瞭粒子物理學標準模型(Standard Model)的數學框架。 第六章:經典場論到量子場論的躍遷 量子力學將粒子視為概率波包,而量子場論(QFT)則將粒子視為場的量子激發。 1. 二次量子化:通過將經典場量提升為算符,引入産生(Creation)和湮滅(Annihilation)算符。 2. 真空態與粒子定義:精確定義真空態,並展示這些算符如何構建多粒子態。 3. 相對論性量子場論的挑戰:引入Klein-Gordon方程和Dirac方程,分析自由場論的構建過程,並初步討論因果性問題。 第七章:相互作用與微擾論——費曼圖的誕生 真實的物理世界充滿瞭相互作用。本章將聚焦於如何量化這些相互作用: 1. 相互作用繪景與S矩陣:定義散射過程的概率幅,即S矩陣。 2. Dyson級數展開:利用微擾論將S矩陣展開,展示其係統性的結構。 3. 費曼規則的建立:通過將Dyson級數的每一項與特定的費曼圖對應起來,將抽象的積分運算轉化為一套清晰的圖形化規則,這是計算高階過程的基石。 第八章:規範場論的普適性 規範對稱性是描述基本相互作用力的核心原則。 1. 從Abelian到Non-Abelian規範群:從電磁學的U(1)規範群(電弱理論的前身)推廣到SU(2)和SU(3)等非阿貝爾群。 2. 規範場與規範玻色子:解釋如何通過要求場論對局域規範變換保持不變性,從而唯一地確定齣傳遞相互作用的玻色子(如光子、膠子)。 3. 重整化基礎:簡要介紹紫外發散問題的齣現,以及重整化程序——物理學中最成功的“修補”技術——如何使理論在有限能量尺度內具有預測能力。 第四部分:時空與信息的交織 本部分探討理論物理學中新興的、跨學科的領域,它們正在重新定義我們對信息、引力和量子力學的理解。 第九章:幾何與拓撲的現代應用 本章將視野從四維時空擴展到更高維空間,並關注拓撲結構在物理學中的作用: 1. 拓撲絕緣體:利用拓撲不變量(如陳數)來描述材料的能帶結構,解釋為何邊緣態具有魯棒的保護性。 2. 霍爾效應的量子化:從拓撲角度理解朗道能級與量子霍爾效應的精確量化。 第十章:信息論與量子計算的前沿 現代物理學日益關注信息在物理係統中的角色。 1. 量子信息基礎:介紹量子比特(Qubit)、量子糾纏(Entanglement)的概念,並討論馮·諾依曼熵與糾纏熵的區彆。 2. 黑洞熱力學與信息悖論:迴顧Bekenstein對黑洞熵的奠基性工作,並分析霍金輻射帶來的信息丟失問題,探討其對時空局部性的衝擊。 3. 信息與引力的聯係:討論AdS/CFT對偶的概念,它暗示瞭引力理論可能(在某些背景下)可以從一個低一維的、純粹的量子場論中“湧現”齣來,突顯信息如何可能成為時空結構的基本要素。 本書旨在通過這種結構化的、由淺入深的論述,引導讀者構建起一個堅實的理論物理學知識體係,使其能夠理解和參與到當代物理學中最激動人心的探索之中。