Introduction to the Classical Theory of Particles and Fields

✍ Scribed by Boris Pavlovich Kosyakov

• Publisher: Springer-Verlag
• Year: 2007
• Tongue: English
• Leaves: 495
• Edition: 1
• Category: Library

✦ Synopsis

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. Two theories covered by the book in great detail are the Maxwell-Lorentz electrodynamics and Yang-Mills-Wong theory.

✦ Table of Contents

Cover......Page 1
Title Page......Page 5
Preface......Page 7
Contents......Page 13
1.1 Spacetime......Page 17
1.2 Affine and Metric Structures......Page 26
1.3 Vectors, Tensors, and n-Forms......Page 38
1.4 Lines and Surfaces......Page 48
1.5 Poincaré Invariance......Page 54
1.6 World Lines......Page 59
Notes......Page 64
2 Relativistic Mechanics......Page 67
2.1 Dynamical Law for Relativistic Particles......Page 68
2.2 The Minkowski Force......Page 74
2.3 Invariants of the Electromagnetic Field......Page 81
2.4 Motion of a Charged Particle in Constant and Uniform Electromagnetic Fields......Page 85
2.5 The Principle of Least Action. Symmetries and Conservation Laws......Page 91
2.6 Reparametrization Invariance......Page 106
2.7 Spinning Particle......Page 114
2.8 Relativistic Kepler Problem......Page 120
2.9 A Charged Particle Driven by a Magnetic Monopole......Page 126
2.10 Collisions and Decays......Page 129
Notes......Page 134
3 Electromagnetic Field......Page 139
3.1 Geometric Contents of Maxwell's Equations......Page 140
3.2 Physical Contents of Maxwell's Equations......Page 143
3.3 Other Forms of Maxwell's Equations......Page 151
Notes......Page 155
4.1 Statics......Page 157
4.2 Solutions to Maxwell's Equations: Some General Observations......Page 168
4.3 Free Electromagnetic Field......Page 173
4.4 The Retarded Green's Function......Page 183
4.5 Covariant Retarded Variables......Page 190
4.6 Electromagnetic Field Generated by a Single Charge Moving Along an Arbitrary Timelike World Line......Page 195
4.7 Another Way of Looking at Retarded Solutions......Page 199
4.8 Field Due to a Magnetic Monopole......Page 203
Notes......Page 207
5.1 Action Principle. Symmetries and Conservation Laws......Page 211
5.2 Poincaré Invariance......Page 222
5.3 Conformal Invariance......Page 232
5.4 Duality Invariance......Page 241
5.5 Gauge Invariance......Page 244
5.6 Strings and Branes......Page 251
Notes......Page 261
6.1 Rearrangement of Degrees of Freedom......Page 265
6.2 Radiation......Page 274
6.3 Energy-Momentum Balance......Page 281
6.4 The Lorentz-Dirac Equation......Page 290
6.5 Alternative Methods of Deriving the Equation of Motion for a Dressed Charged Particle......Page 294
Notes......Page 299
7.1 The Yang–Mills–Wong Theory......Page 301
7.2 The Standard Model......Page 310
7.3 Lattice Formulation of Gauge Theories......Page 314
Notes......Page 321
8 Solutions to the Yang-Mills Equations......Page 323
8.1 The Yang-Mills Field Generated by a Single Quark......Page 325
8.2 Ansatz......Page 333
8.3 The Yang–Mills Field Generated by Two Quarks......Page 336
8.4 The Yang–Mills Field Generated by N Quarks......Page 342
8.5 Stability......Page 347
8.6 Vortices and Monopoles......Page 350
8.7 Two Phases of the Subnuclear Realm......Page 359
Notes......Page 364
9.1 Rearrangement of the Yang–Mills–Wong Theory......Page 369
9.2 Self-Consistency......Page 374
9.3 Paradoxes......Page 376
Notes......Page 381
10.1 Rigid Particle......Page 383
10.2 Different Dimensions......Page 388
10.2.1 Two Dimensions......Page 390
10.2.2 Six Dimensions......Page 392
10.3 Is the Dimension D = 3 Indeed Distinguished?......Page 399
10.4 Nonlinear Electrodynamics......Page 401
10.5 Nonlocal Interactions......Page 409
10.6 Action at a Distance......Page 417
Notes......Page 423
A. Differential Forms......Page 427
B. Lie Groups and Lie Algebras......Page 432
C. The Gamma Matrices and Dirac Spinors......Page 439
D. Conformal Transformations......Page 443
E. Grassmannian Variables......Page 450
F. Distributions......Page 453
Notes......Page 462
B......Page 465
C......Page 467
D......Page 468
F......Page 469
G......Page 470
H......Page 471
K......Page 473
L......Page 474
M......Page 475
N......Page 476
P......Page 477
S......Page 479
T......Page 481
W......Page 482
Y......Page 483
Z......Page 484
Index......Page 485