PRINCIPLES OF PHYSICS: FROM QUANTUM FIELD THEORY TO CLASSICAL MECHANICS (Tsinghua Report and Review in Physics)

This book starts from a set of common basic principles to establish the formalisms in all areas of fundamental physics, including quantum field theory, quantum mechanics, statistical mechanics, thermodynamics, general relativity, electromagnetic field, and classical mechanics. Instead of the traditional pedagogic way, the author arranges the subjects and formalisms in a logical-sequential way, i.e. all the formulas are derived from the formulas before them. The formalisms are also kept self-contained. Most of the required mathematical tools are also given in the appendices. Although this book covers all the disciplines of fundamental physics, the book is concise and can be treated as an integrated entity. This is consistent with the aphorism that simplicity is beauty, unification is beauty, and thus physics is beauty. The book may be used as an advanced textbook by graduate students. It is also suitable for physicists who wish to have an overview of fundamental physics. Readership: This is an advanced graduate or postgraduate level book. Front cover 1 Preface 8 Contents 10 1. Basic Principles 18 2. Quantum Fields 20 2.1 Commutators 20 2.2 The equations of motion 29 2.3 Scalar field 38 2.4 The complex scalar field 49 2.5 Spinor fermions 53 2.6 Vector bosons 82 2. 7 Interaction 105 3. Quantum Fields in the Riemann Spacetime 114 3.1 Lagrangian in the Riemann spacetime 114 3.2 Homogeneity of spacetime 116 3.3 Einstein equations 118 3.4 The generator of time translation 119 3.5 The relations of terms in the total action 122 3.6 Interactions 123 4. Symmetry Breaking 126 4.1 Scale invariance 126 4.2 Ground state energy 130 4.3 Symmetry breaking 132 4.4 The Higgs mechanism 135 4.5 Mass and interactions of particles 137 5. Perturbative Field Theory 140 5.1 Invariant commutation relations 140 5.2 n-point Green's function 147 5.3 Interacting scalar field 156 5.4 Divergency in n-point functions 167 5.5 Dimensional regularization 170 5.6 Renormalization 174 5.7 Effective potential 177 6. From Quantum Field Theory to Quantum Mechanics 186 6.1 Non-relativistic limit of the Klein-Gordon equation 186 6.2 Non-relativistic limit of the Dirac equation 188 6.3 Spin-orbital coupling 190 6.4 The operator of time translation in quantum mechanics 192 6.5 Transformation of basis 194 6.6 One-body operators 198 6. 7 Schrodinger equation 200 7. Electromagnetic Field 204 7.1 Current density 204 7.2 Classical limit 206 7.3 Maxwell equations 207 7.4 Gauge invariance 208 7.5 Radiation of electromagnetic waves 208 7.6 Poisson equation 210 7. 7 Electrostatic energy of charges 211 7.8 Many-body operators 212 7.9 Potentials of charge particles in the classical limit 214 8. Quantum Mechanics 216 8.1 Equations of motion for operators in quantum mechanics 216 8.2 Elementary aspects of the Schrodinger equation 220 8.3 Newton's law 222 8.4 Lorentz force 224 8.5 Path integral formalism for quantum mechanics 225 8.6 Three representations 233 8.7 S Matrix 237 8.8 de Broglie waves 238 8.9 Statistical interpretation of wave functions 240 8.10 Heisenberg uncertainty principle 241 8.11 Stationary states 245 9. Applications of Quantum Mechanics 248 9.1 Harmonic oscillator 248 9.2 Schrodinger equation for a central potential 253 10. Statistical Mechanics 268 10.1 Equi-probability principle and statistical distributions 268 10.2 Average of an observable  271 10.3 Functional integral representation of partition function 273 10.4 First law of thermodynamics 274 10.5 Second law of thermodynamics 276 10.6 Third law of thermodynamics 289 10.7 Thermodynamic quantities expressed in terms of grand partition function 290 10.8 Relation between grand partition function and partition function 292 10.9 Systems with particle number changeable 293 10.10 Equilibrium distributions of nearly independent particle systems 296 10.11 Fluctuations 305 10.12 Classic statistical mechanics and quantum corrections 308 11. Applications of Statistical Mechanics 318 11.1 Ideal gas 318 11.2 Weakly degenerate quantum gas 328 11.3 Bose gas 331 11.4 Photon gas 336 11.5 Fermi gas 339 12. General Relativity 346 12.1 Classical energy-momentum tensor 346 12.2 Equation of motion in the Riemann spacetime 349 12.3 Weak field limit 351 12.4 Spherical solutions for stars 360 12.5 White dwarfs 373 12.6 Neutron Stars 376 Appendices 382 Appendix A. Tensors 382 Appendix B. Functional Formula 402 Appendix C. Gaussian Integrals 404 Appendix D. Grassmann Algebra 408 Appendix E. Euclidean Representation 414 Appendix F. Some Useful Formulas 416 Appendix G. Jacobian 420 Appendix H. Geodesic Equation 422 Bibliography 426 Index 430 Back cover 446 Basic Principles -- Quantum Fields -- Quantum Fields In The Riemann Spacetime -- Symmetry Breaking -- Perturbative Field Theory -- From Quantum Field Theory To Quantum Mechanics -- Electromagnetic Field -- Quantum Mechanics -- Applications Of Quantum -- Statistical Mechanics -- Applications Of Statistical Mechanics -- General Relativity. Jun Ni, Tsinghua University, China. Includes Bibliographical References (pages 409-411) And Index.