Kosyakov Introduction to the Classical Theory of Particles and Fields

1. Auflage 2007
ISBN: 978-3-540-40934-2
Verlag: Springer Berlin Heidelberg
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 479 Seiten

This volume is intended as a systematic introduction to gauge field theory for advanced undergraduate and graduate students in high energy physics. The discussion is restricted to the classical (non-quantum) theory in Minkowski spacetime. Particular attention has been given to conceptual aspects of field theory, accurate definitions of basic physical notions, and thorough analysis of exact solutions to the equations of motion for interacting systems.

Autoren/Hrsg.

Kosyakov, Boris

Inhaltsverzeichnis

1;Preface;5
2;Contents;10
3;1 Geometry of Minkowski Space;13
3.1;1.1 Spacetime;13
3.2;1.2 Affine and Metric Structures;22
3.3;1.3 Vectors, Tensors, and n-Forms;34
3.4;1.4 Lines and Surfaces;44
3.5;1.5 Poincare Invariance;50
3.6;1.6 World Lines;55
3.7;Notes;60
4;2 Relativistic Mechanics;63
4.1;2.1 Dynamical Law for Relativistic Particles;64
4.2;2.2 The Minkowski Force;70
4.3;2.3 Invariants of the Electromagnetic Field;77
4.4;2.4 Motion of a Charged Particle in Constant and Uniform Electromagnetic Fields;81
4.5;2.5 The Principle of Least Action. Symmetries and Conservation Laws;87
4.6;2.6 Reparametrization Invariance;102
4.7;2.7 Spinning Particle;110
4.8;2.8 Relativistic Kepler Problem;116
4.9;2.9 A Charged Particle Driven by a Magnetic Monopole;122
4.10;2.10 Collisions and Decays;125
4.11;Notes;130
5;3 Electromagnetic Field;134
5.1;3.1 Geometric Contents of Maxwell’s Equations;135
5.2;3.2 Physical Contents of Maxwell’s Equations;138
5.3;3.3 Other Forms of Maxwell’s Equations;146
5.4;Notes;150
6;4 Solutions to Maxwell’s Equations;152
6.1;4.1 Statics;152
6.2;4.2 Solutions to Maxwell’s Equations: Some General Observations;163
6.3;4.3 Free Electromagnetic Field;168
6.4;4.4 The Retarded Green’s Function;178
6.5;4.5 Covariant Retarded Variables;185
6.6;4.6 Electromagnetic Field Generated by a Single Charge Moving Along an Arbitrary Timelike World Line;190
6.7;4.7 Another Way of Looking at Retarded Solutions;194
6.8;4.8 Field Due to a Magnetic Monopole;198
6.9;Notes;202
7;5 Lagrangian Formalism in Electrodynamics;205
7.1;5.1 Action Principle. Symmetries and Conservation Laws;205
7.2;5.2 Poincare Invariance;216
7.3;5.3 Conformal Invariance;226
7.4;5.4 Duality Invariance;235
7.5;5.5 Gauge Invariance;238
7.6;5.6 Strings and Branes;245
7.7;Notes;255
8;6 Self-Interaction in Electrodynamics;259
8.1;6.1 Rearrangement of Degrees of Freedom;259
8.2;6.2 Radiation;268
8.3;6.3 Energy-Momentum Balance;275
8.4;6.4 The Lorentz–Dirac Equation;284
8.5;6.5 Alternative Methods of Deriving the Equation of Motion for a Dressed Charged Particle;288
8.6;Notes;293
9;7 Lagrangian Formalism for Gauge Theories;295
9.1;7.1 The Yang–Mills–Wong Theory;295
9.2;7.2 The Standard Model;304
9.3;7.3 Lattice Formulation of Gauge Theories;308
9.4;Notes;315
10;8 Solutions to the Yang–Mills Equations;317
10.1;8.1 The Yang–Mills Field Generated by a Single Quark;319
10.2;8.2 Ansatz;327
10.3;8.3 The Yang–Mills Field Generated by Two Quarks;330
10.4;8.4 The Yang–Mills Field Generated by N Quarks;336
10.5;8.5 Stability;341
10.6;8.6 Vortices and Monopoles;344
10.7;8.7 Two Phases of the Subnuclear Realm;353
10.8;Notes;358
11;9 Self-Interaction in Gauge Theories;362
11.1;9.1 Rearrangement of the Yang–Mills–Wong Theory;362
11.2;9.2 Self-Consistency;367
11.3;9.3 Paradoxes;369
11.4;Notes;374
12;10 Generalizations;376
12.1;10.1 Rigid Particle;376
12.2;10.2 Different Dimensions;381
12.3;10.3 Is the Dimension D = 3 Indeed Distinguished?;392
12.4;10.4 Nonlinear Electrodynamics;394
12.5;10.5 Nonlocal Interactions;402
12.6;10.6 Action at a Distance;410
12.7;Notes;416
13;Mathematical Appendices;419
13.1;A. Differential Forms;419
13.2;B. Lie Groups and Lie Algebras;424
13.3;C. The Gamma Matrices and Dirac Spinors;431
13.4;D. Conformal Transformations;435
13.5;E. Grassmannian Variables;442
13.6;F. Distributions;445
13.7;Notes;454
14;References;456
15;Index;476