Author(s): R. Aldrovandi, J. G. Pereira
Series: Lecture notes
Publisher: Instituto de Física Teorica Universida de Estadual Paulista Sao Paulo - Brazil
Year: 2019
Language: English
Pages: 222
Introduction......Page 5
Classical Mechanics......Page 6
Hints Toward Relativity......Page 14
Relativistic Spacetime......Page 16
Lorentz Vectors and Tensors......Page 31
Particle Dynamics......Page 33
Transformation Groups......Page 42
Orthogonal Transformations......Page 46
The Group of Rotations......Page 52
The Poincaré Group......Page 59
The Lorentz Group......Page 60
Introducing Fields......Page 71
The Standard Prototype......Page 72
Non-Material Fields......Page 79
Optional reading: the Quantum Line......Page 81
Wavefields......Page 83
Internal Transformations......Page 84
General Formalism......Page 89
Relativistic Lagrangians......Page 93
Simplified Treatment......Page 95
Rules of Functional Calculus......Page 97
Variations......Page 99
The First Noether Theorem......Page 103
Symmetries and Conserved Charges......Page 105
The Basic Spacetime Symmetries......Page 108
Internal Symmetries......Page 112
The Second Noether Theorem......Page 114
Topological Conservation Laws......Page 117
Real Scalar Fields......Page 121
Complex Scalar Fields......Page 124
Vector Fields......Page 129
Real Vector Fields......Page 130
Complex Vector Fields......Page 133
Maxwell's Equations......Page 136
Transformations of and......Page 138
Covariant Form of Maxwell's Equations......Page 144
Lagrangian, Spin, Energy......Page 147
Motion of a Charged Particle......Page 150
Electrostatics and Magnetostatics......Page 155
Electromagnetic Waves......Page 159
Dirac Equation......Page 166
Non-Relativistic Limit: Pauli Equation......Page 171
Covariance......Page 174
Lagrangian Formalism......Page 180
Parity......Page 181
Charge Conjugation......Page 183
Time Reversal and CPT......Page 185
Introduction......Page 188
The Notion of Gauge Symmetry......Page 191
Global Transformations......Page 192
Local Transformations......Page 193
Local Noether Theorem......Page 195
Field Strength and Bianchi Identity......Page 197
Gauge Lagrangian and Field Equation......Page 198
Final Remarks......Page 201
General Concepts......Page 205
The Equivalence Principle......Page 206
Pseudo-Riemannian Metric......Page 208
The Notion of Connection......Page 209
Curvature and Torsion......Page 210
The Levi-Civita Connection......Page 211
Geodesics......Page 212
Bianchi Identities......Page 213
Einstein's Field Equations......Page 214
The Schwarzschild Solution......Page 215
Index......Page 216
