Gauge field theories : an introduction with applications / Mike Guidry.

Format:

Book

Author/Creator:

Guidry, M. W. (Michael Wayne)

Language:

English

Subjects (All):

Gauge fields (Physics).

Quantum field theory.

Physical Description:

xv, 605 pages : illustrations ; 24 cm

Place of Publication:

New York : Wiley, [1991]

Summary:

This book acquaints readers with the main concepts and literature of elementary particle physics and quantum field theory. Divided into three parts, it opens with an introduction to the general principles of relativistic quantum field theory, followed by the essential ingredients of gauge fields for weak and electromagnetic interactions, quantum chromodynamics and strong interactions. The third part deals with the interface between modern elementary particle physics and "applied disciplines" such as nuclear physics, astrophysics, and cosmology.

Contents:

Part I Quantum Field Theory

1. Relativistic Wave Equations 3

1.1 Special Relativity and Spacetime 3

1.2 Contravariant and Covariant Vectors 4

1.3 Lorentz Transformations 9

1.4 Klein-Gordon Equation 14

1.5 Dirac Equation 17

1.6 Prescriptions for Negative-Energy States 30

1.7 Feynman Diagrams 39

1.8 Loops, Trees, and Infinities 46

2. Canonical Quantization of Local Field Theories 49

2.1 Quantization in Discrete Mechanics 50

2.2 General Properties of the Action 55

2.3 Lagrangian Densities for Free Fields 56

2.4 Quantization of the Real Scalar Field 60

2.5 Quantization of a Complex Scalar Field 68

2.6 Quantization of the Dirac Field 69

2.7 Quantization of the Electromagnetic Field 74

2.8 Noether's Theorem 89

2.9 Interactions between Fields 94

3. Perturbation Theory and Evaluation of the S-Matrix 96

3.1 Interaction Representation 96

3.2 Definition of the S-Matrix 98

3.3 Interaction Picture Fourier Expansions 101

3.4 Reduction by Wick's Theorem 103

3.5 Example: Self-Coupled Scalar Field 112

3.6 Differential Cross Sections 122

3.7 Example: Spinor Electrodynamics 123

3.8 Graphs That Are Excluded 128

3.9 Feynman Rules for Electrodynamics 128

4. Path Integral Quantization 135

4.1 Nonrelativistic Path Integral 135

4.2 Path Integral for Field Theory 139

4.3 Evaluation of Path Integrals 146

4.4 Feynman Diagrams 149

4.5 Grassmann Variables 150

4.6 Fermions in the Path Integral 151

4.7 Ghost Fields 153

Part II Gauge Field Theories

5. Symmetry and Group Theory 157

5.1 Introduction to the Theory of Groups 157

5.2 Lie Groups and Lie Algebras 163

5.3 Unitary Symmetries 167

5.4 Topological Properties 199

6. Weak and Electromagnetic Interactions 201

6.1 QED: Prototype Quantum Field Theory 202

6.2 Phenomenology of the Weak Interactions 206

6.3 Problems with the Fermi Phenomenology 215

6.4 Renormalization in QED 221

6.5 Renormalization and Weak Interactions 232

7. Yang

Mills Fields 234

7.1 Local Non-Abelian Gauge Invariance 234

7.2 Properties of Yang

Mills Fields 237

7.3 Path-Dependent Representations 239

7.4 Path Integral Quantization 241

8. Spontaneously Broken Symmetry and the Higgs Mechanism 246

8.1 Classical Symmetry Modes 246

8.2 A Simple Example 248

8.3 Goldstone Bosons 251

8.4 The Higgs Mechanism 256

8.5 Some General Remarks 260

9. Standard Electroweak Model 266

9.1 The Electroweak Gauge Group 266

9.2 Standard Model for Leptonic Interactions 269

9.3 Inclusion of Hadrons 280

9.4 Critique of the Standard Theory 285

10. The Strong Interactions and Quantum Chromodynamics 287

10.1 Properties of Quarks 287

10.2 Evidence for Gluons 293

10.3 Deep Inelastic Lepton Scattering 294

10.4 Partons 299

10.5 The Quark-Parton Model 302

10.6 Quantum Chromodynamics 309

11. Grand Unified Theories 321

11.1 Evolution of Coupling Constants 323

11.2 Minimal Criteria for a GUT Group 324

11.3 The SU (5) Grand Unified Theory 325

11.4 Decay of the Proton 328

Part III Models and Applications

12. Models for QCD 333

12.1 Confinement Phenomenology 333

12.2 Current Algebra and Chiral Symmetry 339

12.3 Linear [sigma]-Model 341

12.4 Chiral SU(3) [times] SU(3) Symmetry 347

12.5 Bag Models 349

12.6 Nonrelativistic Potential Models 375

13. Non-Perturbative Methods in Gauge Field Theories 387

13.1 Lattice Gauge Theory 387

13.2 Topology of Group Manifolds 419

13.3 Solitons in (1+1) Dimensions 423

13.4 Quantization of Solitons 435

13.5 More Dimensions and Derrick's Theorem 436

13.6 Topological Conservation Laws in (2+1) and (3+1) Dimensions 437

13.7 Yang-Mills Instantons 440

13.8 Skyrmions 448

14. Deconfined Quarks and Gluons 456

14.1 Deconfining and Chiral Phase Transitions 456

14.2 Simple Thermodynamical Considerations 460

14.3 Debye Screening in the Plasma 464

14.4 Finite Temperature Yang-Mills Theory 466

14.5 Chiral Phase Transition 472

14.6 Hydrodynamics at 1 GeV/Nucleon 476

14.7 Ultrarelativistic Hydrodynamics 477

14.8 Production of Baryon-Poor Plasmas 482

14.9 Experimental Evidence 482

15. Cosmology and Gauge Theories 487

15.1 The Hot Big Bang 487

15.2 Baryogenesis 493

15.3 Problems with the Hot Big Bang 497

15.4 Inflationary Cosmologies 500

A. Natural Units 511

B. Hadronic Properties 515

C. Relativistic Kinematic Variables 517.

Notes:

"A Wiley-Interscience publication."

Includes bibliographical references (pages 579-592) and index.

ISBN:

0471631175

OCLC:

22309707