Mathematical and Conceptual Foundations of 20th-Century Physics (eBook)

Front Cover 1
Mathematical and Conceptual Foundations of 20th-Century Physics 4
Copyright Page 5
Contents 6
Preface 9
PART I. CLASSICAL PHYSICS 12
Chapter 1. Mechanics 12
1. Newtonian formulation 14
2. Lagrangean formulation 26
3. Hamiltonian formulation 34
Chapter 2. Thermodynamics and Statistical Mechanics 42
1. Temperature and heat 44
2. Classical statistical mechanics 59
Chapter 3. Electromagnetism 78
1. Phenomenological background 79
2. The nature of light 90
PART II. RELATIVITY 102
Chapter 4. Geometry 102
1. Galilean and Minkowskian geometries 102
2. Curved space-time geometries 112
Chapter 5. The Principles of Special Relativity 144
1. Formulation of the principles 145
2. Immediate consequences of the principles 156
Chapter 6. General Relativity 172
1. Models for space-time 172
2. Electromagnetism revisited 197
3. Models for matter 202
PART III. QUANTUM THEORY 220
Chapter 7. The ‘old’ quantum theory 220
1. Black-body radiation 222
2. Electrons, photons and phonons 231
3. The structure of the atom 243
Chapter 8. Hilbert space formulation of quantum mechanics 260
1. The Heisenberg matrix formulation 263
2. The Schroedinger wave mechanics 287
3. Von Neumann’s Hilbert space formalism 306
4. Quantum scattering theory 356
Chapter 9. The algebraic formulation of quantum mechanics 372
1. The fundamental postulate 373
2. Non-commutative ergodic theory 394
Chapter 10. Systems with infinitely many degrees of freedom 428
1. Quantum statistical mechanics 428
2. Quantum field theory 511