夸克、輕子和規(guī)范場(chǎng)

前言

According to the current view，the basic building blocks of matter are quarks and leptons，which interact with one another through the intermediaries of Yang. Mills gauge fields （gravity being ignored in this context）.This means that the forms of the interactions are completely determined by the algebraic structure of certain internal symmetry groups.Thus，the strong interactions are associated with the group SU（3），and iS described by a gauge theory called quantum chromodynamics.The electro.weak interactions.as described by the now start. dard Weinberg-Salam model，iS associated with the group su（2）×U（1）.This book iS a concise introduction to the physical motivation behind these ideas，and precise mathematical formulation thereof.The goal of the book iS to explain why and how the mathematical formalism helps US to understand the relevant observed phenomena.The audience for which this book iS written ale graduate students in physics who have some knowledge of the experimental parts of particle physics，and an acquaintance with quantum field theory.including Feynman graphs and the notion of renormalization.This book might serve as a text for a one-semester course beyond quantum field theory.The first edition 0f mis book，which came out in 1982，was based on a course I gave at M.I.T.，and on lectures I gave in Santiago，Chile，in 1977，and in Beiiing，China.in 1979.I am indebted to I.Saavedra for the opportunity to lecture in Chile.to Chang Wen-yu and S.C.C.Ting for the inducement to give the Beijing lecture。and to M.Jacob and K.K.Phua for the encouragement to bring out the first edition.  The main addition to the second edition are Wilson’S approach t0 renormaliza. tion，Iattice gauge theory，and quark confinement.I am grateful to the many readers who have pointed out ell-ors in the first edition.which I hope have been corrected in this edition.I owe special thanks to my colleagues at M.I.T.，especially A.Guth.R. Jackiw，K.Johnson，and J.Polonyi，from whom I have Iearned much that iS being passed along in this book.

內(nèi)容概要

依據(jù)通行的觀點(diǎn)，物質(zhì)的基本徹塊是夸克與輕子，它們通過(guò)楊-米爾斯規(guī)范場(chǎng)的媒介相互作用(在這種場(chǎng)合下引力被忽略了)。這就意味著相互作用的形式是完全由某些內(nèi)部對(duì)稱群的代數(shù)結(jié)構(gòu)所決定的。于是強(qiáng)相互作用是與SU(3)群相關(guān)聯(lián)的，它是由叫做量子色動(dòng)力學(xué)的規(guī)范場(chǎng)理論所描述的。而電一弱相互作用則是與SU(2)XU(1)群相關(guān)聯(lián)的，現(xiàn)在它是由標(biāo)準(zhǔn)的溫伯格-薩拉姆模型來(lái)描述的。本書簡(jiǎn)明地介紹了在這些思想背后的動(dòng)力，以及由此而來(lái)的嚴(yán)謹(jǐn)?shù)臄?shù)學(xué)系統(tǒng)表述。

作者簡(jiǎn)介

作者：(美國(guó))黃克遜

書籍目錄

PREFACEⅠ.INTRODUCTION  1.1 Particles and Interactions  1.2 Gauge Theories of Interactions  1.3 Notations and ConventionsⅡ.QUARKS  2.1 Internal Symmetries    1 Isospin    2 The gauge groups    3 More general internal symmetries: SU(n)    4 Unitary symmetry  2.2 Representation of SU(3)    1 The basic representation    2 Young's tableaux    3 Irreducible representations  2.3 The Quark Model    1 Quarks as basic triplets    2 Quarks as building blocks    3 Weight diagrams    4 The composition of hadrons  2.4 Color    1 Independent quark model    2 Color SU(3) group  2.5 Electromagnetic and Weak Probes    1 Electromagnetic interactions    2 Parton model    3 Evidence for color    4 Weak interactions  2.6 Charm    1 The charmed quark    2 The J/φ and its family    3 Correspondence between quarks and leptonsⅢ.MAXWELL FIELD: U(I) GAUGE THEORY  3.1 Global and Local Gauge Invariance  3.2 Spontaneous Breaking of Global Gauge Invariance: Goldstone Mode  3.3 Spontaneous Breaking of Local Gauge Invariance: Higgs Mode  3.4 Classical Finite-Energy Solutions  3.5 Magnetic Flux Quantization  3.6 Soliton Solutions: Vortex LinesⅣ.  YANG-MILLS FIELDS: NON-ABELIAN GAUGE THEORIES  4.1 Introductory Note  4.2 Lie Groups    1 Structure constants    2 Matrix representations    3 Topological properties    4 General remarks  4.3 The Yang-Mills Constructions    1 Global gauge invariance    2 Local gauge invariance  4.4 Properties of Yang-Milis Fields    1 Electric and magnetic fields    2 Dual tensor    3 Path representation of the gauge group  4.5 Canonical Formalism    1 Equations of motion    2 Hamiltonian  4.6 Spontaneous Symmetry Breaking    1 The little group    2 Higgs mechanismⅤ.TOPOLOGICAL SOLITONS  5.1 Solitons  5.2 The Instanton    1 Topological charge    2 Explicit solution  5.3 The Monopole    1 Topological stability    2 Flux quantization    3 Boundary conditions    4 Explicit solution    5 Physical fields    6 Spin from isospinⅥ.WEINBERG-SALAM MODEL  6.1 The Matter Fields  6.2 The Gauge Fields    1 Gauging SU(2)×U(1)    2 Determination of constants    3 Interactions  6.3 The General Theory    1 Mass terms    2 Cabibbo angle    3 Kobayashi-Maskawa matrix    4 SolitonsⅦ.METHOD OF PATH INTEGRALS  7.1 Non-Relativistic Quantum Mechanics  7.2 Quantum Field Theory  7.3 External Sources  7.4 Euclidean 4-Space  7.5 Calculation of Path Integrals  7.6 The Feynman .Propagator  7.7 Feynman Graphs  7.8 Boson Loops and Fermion Loops  7.9 Fermion FieldsⅧ.QUANTIZATION OF GAUGE FIELDS  8.1 Canonical Quantization    1 Free Maxwell field    2 Pure Yang-Mills fields  8.2 Path Integral Method in Hamiltonian Form  8.3 Feynman Path Integral: Fadeev-Popov Method  8.4 Free Maxwell Field    1 Lorentz gauge    2 Coulomb gauge    3 Temporal and axial gauges  8.5 Pure Yang-Mills Fields    I Axial gauge    2 Lorentz gauge: Fadeev-Popov ghosts  8.6 The 0-World and the Instanton    1 Discovering the 0-world    2 lnstanton as tunneling solution    3 The 0-action  8.7 Gribov Ambiguity  8.8 Projection Operator for Gauss' LawⅨ.RENORMALIZATION  9.1 Charge Renormalization  9.2 Perturbative Renormalization in Quantum Electredynamics  9.3 The Renormalization Group    1 Scale transformations    2 Scaling form    3 Fixed points    4 Callan-Symanzik equation  9.4 Scalar Fields    1 Renormalizability    2 Φ4 theory    3 "Triviality" and the Landau ghost  9.5 The Physics of Renormalization    1 Renormalization-group transformation    2 Real-space renormalization    3 Fixed points and relevancy    4 Renormalization and universality  Appendix to Chapter 9. Renormalization of QED    1 Vertex    2 Electron Propagator    3 Photon Propagator    4 Scaling Properties    5 Renormalization    6 Gauge Invariance and the Photon MassⅩ.METHOD OF EFFECTIVE POTENTIAL  10.1 Spontaneous Symmetry Breaking  10.2 The Effective Action  10.3 The Effective Potential  10.4 The Loop Expansion  10.5 One-Loop Effective Potential  10.6 Renormalization    1 General scheme    2 Massive case    3 Massless case  10.7 Dimensional Transmutation  10.8 A Non-Relativistic Example  10.9 Application to Weinberg-Salam ModelⅪ. THE AXIAL ANOMALY  11.1 Origin of the Axial Anomaly  11.2 The Triangle Graph  11.3 Anomalous Divergence of the Chiral Current  11.4 Physical Explanation of the Axial Anomaly  11.5 Cancellation of Anomalies  11.6 't Hooft's PrincipleⅫ.  QUANTUM CHROMODYNAMICS  12.1 General Properties    1 Lagrangian density    2 Feynman rules    3 Quark-gluon interactions    4 Gluon self-interactions  12.2 The Color Gyromagnetic Ratio  12.3 Asymptotic Freedom    1 The running coupling constant    2 The vacuum as magnetic medium    3 The Nielsen-Hughes formula  12.4 The Pion as Goldstone Boson     1 The low-energy domain    2 Chiral symmetry: an idealized limit    3 PCAC    4 The decay π0→2y    5 Extension to pion octet  12.5 The U(1) Puzzle  12.6 θ-Worlds in QCD    1 Euclidean action    2 The axial anomaly and the index theorem    3 Chiral limit: Collapse of the 0-worlds    4 Quark mass matrix    5 Strong CP violationⅩⅢ. LATTICE GAUGE THEORY  13.1 Wilson's Lattice Action  13.2 Transfer Matrix  13.3 Lattice Hamiltonian  13.4 Lattice Fermions  13.5 Wilson Loop and Confinement  13.6 Continuum Limit  13.7 Monte Carlo MethodsⅩⅣ. QUARK CONFINEMENT  14.1 Wilson Criterion and Electric Confmement  14.2 String Model of Hadrons  14.3 Superconductivity: Magnetic Confinement    1 Experimental manifestation    2 Theory    3 Mechanism for monopole confinement  14.4 Electric and Magnetic Order Parameters  14.5 Scenario for Quark Confinement  Appendix to Chapter 14.Symmetry and Confinement    1 Quark Propagator    2 Center Symmetry    3 Confinement as SymmetryINDEX

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