Gauge Theory of Elementary Particle Physics

This is a practical introduction to the principal ideas in gauge theory and their applications to elementary particle physics. It explains technique and methodology with simple exposition backed up by many illustrative examples. Derivations, some of well

PART I

Basics in field quantization

Review of canonical quantization formalism

4

(7)

Introduction to path integral formalism

11

(11)

Fermion field quantization

22

(9)

Introduction to renormalization theory

Conventional renormalization in λ &phis; theory

31

(8)

BPH renormalization in λ &phis; theory

39

(6)

Regularization schemes

45

(11)

Power counting and renormalizability

56

(11)

Renormalization group

Momentum subtraction schemes and the Callan-Symanzik equation

67

(10)

The minimal subtraction scheme and its renormalization-group equation

77

(4)

Effective coupling constants

81

(5)

Group theory and the quark model

Elements of group theory

86

(4)

SU(2) and SU(3)

90

(12)

The tensor method in SU(n)

102

(11)

The quark model

113

(13)

Chiral symmetry of the strong interaction

Global symmetries in field theory and current commutators

126

(8)

Symmetry currents as physical currents

134

(7)

Spontaneous breaking of global symmetry, the Goldstone theorem

141

(10)

PCAC and soft pion theorems

151

(9)

Pattern of chiral symmetry breaking

160

(9)

Renormalization and symmetry

The vector-current Ward identity and renormalization

169

(4)

Axial-vector-current Ward identity anomaly and π0 ← 2y

173

(9)

Renormalization in theories with spontaneous symmetry breaking

182

(7)

The effective potential and radiatively induced spontaneous symmetry breakdown

189

(10)

The Parton model and scaling

The parton model of deep inelastic lepton-hadron scattering

199

(9)

Sum rules and applications of the quark-parton model

208

(10)

Free-field light-cone singularities and Bjorken scaling

218

(11)

PART II

Gauge symmetries

Local symmetries in field theory

229

(6)

Gauge invariance and geometry

235

(5)

Spontaneous breaking of gauge symmetry, the Higgs phenomenon

240

(8)

Quantum gauge theories

Path-integral quantization of gauge theories

248

(9)

Feynman rules in covariant gauges

257

(10)

The Slavnov-Taylor identities

267

(13)

Quantum chromodynamics

The discovery of asymptotic freedom

280

(11)

The QCD Lagrangian and the symmetries of the strong interaction

291

(4)

Renormalization group analysis of scaling and scaling violation

295

(16)

The parton model and perturbative QCD

311

(11)

Lattice gauge theory and colour confinement

322

(14)

Standard electroweak theory I: basic structure

Weak interactions before gauge theories

336

(3)

Construction of the standard SU(2) x U(1) theory

339

(16)

Fermion family replication

355

(9)

Standard electroweak theory II: phenomenological implications

Flavour-conserving neutral-current processes

364

(7)

Weak mixing angles, the GIM mechanism, and CP violation

371

(15)

The W and Z intermediate vector bosons

386

(8)

The Higgs particle

394

(7)

Selected topics in quantum flavourdynamics

Dynamical symmetry breaking and technicolour models

401

(8)

Neutrino masses, mixings and oscillations

409

(11)

μ ← ey, An example of Rξ gauge loop calculations

420

(8)

Grand unification

Introduction to the SU(5) model

428

(6)

Spontaneous symmetry breaking and gauge hierarchy

434

(3)

Coupling constant unification

437

(5)

Proton decay and baryon asymmetry in the universe

442

(5)

Fermion masses and mixing angles in the minimal SU(5) model

447

(6)

Magnetic monopoles

Dirac's theory of magnetic poles

453

(7)

Solitons in field theory

460

(6)

The 't Hooft-Polyakov monopole

466

(10)

Instantons

The topology of gauge transformations

476

(6)

The instanton and vacuum tunnelling

482

(5)

Instantons and the U(1) problem

487

(7)

Appendix A Notations and conventions

494

(4)

Appendix B Feynman rules

498

(15)

Bibliography

513

(4)

References

517

(10)

Subject Index

527

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Gauge Theory of Elementary Particle Physics

Summary

Table of Contents

Supplemental Materials