ADVANCED QUANTUM MECHANICS
IDENTICAL PARTICLES, MANY-PARTICLE STATES, AND PERMUTATION SYMMETRY STATES AND OBSERVABLES OF IDENTICAL PARTICLES EXAMPLES COMPLETELY SYMMETRIC AND ANTISYMMETRIC STATES BOSONS STATES, FOCK SPACE, CREATION AND ANNIHILATION OPERATORS THE PARTICLE-NUMBER OPERATOR GENERAL SINGLE- AND MANY-PARTICLE OPERATORS FERMIONS SINGLE- AND MANY-PARTICLE OPERATORS FIELD OPERATORS TRANSFORMATIONS BETWEEN DI?ERENT BASIS SYSTEMS FIELD EQUATIONS MOMENTUM REPRESENTATION MOMENTUM EIGENFUNCTIONS AND THE HAMILTONIAN FOURIER TRANSFORMATION OF THE DENSITY THE INCLUSION OF SPIN PROBLEMS 2 SPIN-1/2 FERMIONS NONINTERACTING FERMIONS THE FERMI SPHERE, EXCITATIONS SINGLE-PARTICLE CORRELATION FUNCTION PAIR DISTRIBUTION FUNCTION PAIR DISTRIBUTION FUNCTION, DENSITY CORRELATION FUNCTIONS, AND STRUCTURE FACTOR GROUND STATE ENERGY AND ELEMENTARY THEORY OF THE ELECTRON GAS HAMILTONIAN GROUND STATE ENERGY IN THE HARTREE–FOCK APPROXIMATION MODI?CATION OF ELECTRON ENERGY LEVELS DUE TO THE COULOMB INTERACTION HARTREE–FOCK EQUATIONS FOR ATOMS 3 BOSONS FREE BOSONS PAIR DISTRIBUTION FUNCTION FOR FREE BOSONS TWO-PARTICLE STATES OF BOSONS WEAKLY INTERACTING, DILUTE BOSE GAS QUANTUM FLUIDS AND BOSE–EINSTEIN CONDENSATION BOGOLIUBOV THEORY OF THE WEAKLY INTERACTING BOSE GAS SUPER?UIDITY 4 CORRELATION FUNCTIONS, SCATTERING, AND RESPONSE SCATTERING AND RESPONSE DENSITY MATRIX, CORRELATION FUNCTIONS DYNAMICAL SUSCEPTIBILITY DISPERSION RELATIONS SPECTRAL REPRESENTATION FLUCTUATION–DISSIPATION THEOREM EXAMPLES OF APPLICATIONS SYMMETRY PROPERTIES GENERAL SYMMETRY RELATIONS SYMMETRY PROPERTIES OF THE RESPONSE FUNCTION FOR HERMITIAN OPERATORS SUM RULES GENERAL STRUCTURE OF SUM RULES APPLICATION TO THE EXCITATIONS IN HE II BIBLIOGRAPHY FOR PART I PART II RELATIVISTIC WAVE EQUATIONS 5 RELATIVISTIC WAVE EQUATIONS AND THEIR DERIVATION INTRODUCTION THE KLEIN–GORDON EQUATION DERIVATION BY MEANS OF THE CORRESPONDENCE PRINCIPLE THE CONTINUITY EQUATION FREE SOLUTIONS OF THE KLEIN–GORDON EQUATION DIRAC EQUATION DERIVATION OF THE DIRAC EQUATION PROPERTIES OF THE DIRAC MATRICES THE DIRAC EQUATION IN COVARIANT FORM NONRELATIVISTIC LIMIT AND COUPLING TO THE ELECTROMAGNETIC FIELD 6 LORENTZ TRANSFORMATIONS AND COVARIANCE OF THE DIRAC EQUATION LORENTZ TRANSFORMATIONS LORENTZ COVARIANCE OF THE DIRAC EQUATION LORENTZ COVARIANCE AND TRANSFORMATION OF SPINORS DETERMINATION OF THE REPRESENTATION S(?) FURTHER PROPERTIES OF S TRANSFORMATION OF BILINEAR FORMS PROPERTIES OF THE ? MATRICES SOLUTIONS OF THE DIRAC EQUATION FOR FREE PARTICLES SPINORS WITH FINITE MOMENTUM ORTHOGONALITY RELATIONS AND DENSITY PROJECTION OPERATORS 7 ORBITAL ANGULAR MOMENTUM AND SPIN PASSIVE AND ACTIVE TRANSFORMATIONS ROTATIONS AND ANGULAR MOMENTUM 8 THE COULOMB POTENTIAL KLEIN–GORDON EQUATION WITH ELECTROMAGNETIC FIELD COUPLING TO THE ELECTROMAGNETIC FIELD KLEIN–GORDON EQUATION IN A COULOMB FIELD DIRAC EQUATION FOR THE COULOMB POTENTIAL 9 THE FOLDY–WOUTHUYSEN TRANSFORMATION AND RELATIVISTIC CORRECTIONS THE FOLDY–WOUTHUYSEN TRANSFORMATION DESCRIPTION OF THE PROBLEM TRANSFORMATION FOR FREE PARTICLES INTERACTION WITH THE ELECTROMAGNETIC FIELD RELATIVISTIC CORRECTIONS AND THE LAMB SHIFT RELATIVISTIC CORRECTIONS ESTIMATE OF THE LAMB SHIFT 10 PHYSICAL INTERPRETATION OF THE SOLUTIONS TO THE DIRAC EQUATION 10 1 WAVE PACKETS AND “ZITTERBEWEGUNG” 10 1 1 SUPERPOSITION OF POSITIVE ENERGY STATES 10 1 2 THE GENERAL WAVE PACKET ?10 1 3 GENERAL SOLUTION OF THE FREE DIRAC EQUATION IN THE HEISENBERG REPRESENTATION ?10 1 4 POTENTIAL STEPS AND THE KLEIN PARADOX 10 2 THE HOLE THEORY 11 SYMMETRIES AND FURTHER PROPERTIES OF THE DIRAC EQUATION ?11 1 ACTIVE AND PASSIVE TRANSFORMATIONS, TRANSFORMATIONS OF VECTORS 11 2 INVARIANCE AND CONSERVATION LAWS 11 2 1 THE GENERAL TRANSFORMATION 11 2 2 ROTATIONS 11 2 3 TRANSLATIONS 11 2 4 SPATIAL RE?ECTION (PARITY TRANSFORMATION) 11 3 CHARGE CONJUGATION 11 4 TIME REVERSAL (MOTION REVERSAL) 11 4 1 REVERSAL OF MOTION IN CLASSICAL PHYSICS 11 4 2 TIME REVERSAL IN QUANTUM MECHANICS 11 4 3 TIME-REVERSAL INVARIANCE OF THE DIRAC EQUATION ?11 4 4 RACAH TIME RE?ECTION ?11 5 HELICITY ?11 6 ZERO-MASS FERMIONS (NEUTRINOS) BIBLIOGRAPHY FOR PART II PART III RELATIVISTIC FIELDS 12 QUANTIZATION OF RELATIVISTIC FIELDS 12 1 COUPLED OSCILLATORS, THE LINEAR CHAIN, LATTICE VIBRATIONS 12 1 1 LINEAR CHAIN OF COUPLED OSCILLATORS 12 1 2 CONTINUUM LIMIT, VIBRATING STRING 12 1 3 GENERALIZATION TO THREE DIMENSIONS, RELATIONSHIP TO THE KLEIN–GORDON FIELD 12 2 CLASSICAL FIELD THEORY 12 2 1 LAGRANGIAN AND EULER–LAGRANGE EQUATIONS OF MOTION 12 3 CANONICAL QUANTIZATION 12 4 SYMMETRIES AND CONSERVATION LAWS, NOETHER’S THEOREM 12 4 1 THE ENERGY–MOMENTUM TENSOR, CONTINUITY EQUATIONS, AND CONSERVATION LAWS 12 4 2 DERIVATION FROM NOETHER’S THEOREM OF THE CONSERVATION LAWS FOR FOUR-MOMENTUM, ANGULAR MOMENTUM, AND CHARGE 13 FREE FIELDS 13 1 THE REAL KLEIN–GORDON FIELD 13 1 1 THE LAGRANGIAN DENSITY, COMMUTATION RELATIONS, AND THE HAMILTONIAN 13 1 2 PROPAGATORS 13 2 THE COMPLEX KLEIN–GORDON FIELD 13 3 QUANTIZATION OF THE DIRAC FIELD 13 3 1 FIELD EQUATIONS 13 3 2 CONSERVED QUANTITIES 13 3 3 QUANTIZATION 13 3 4 CHARGE ?13 3 5 THE IN?NITE-VOLUME LIMIT 13 4 THE SPIN STATISTICS THEOREM 13 4 1 PROPAGATORS AND THE SPIN STATISTICS THEOREM 13 4 2 FURTHER PROPERTIES OF ANTICOMMUTATORS AND PROPAGATORS OF THE DIRAC FIELD 14 QUANTIZATION OF THE RADIATION FIELD 14 1 CLASSICAL ELECTRODYNAMICS 14 1 1 MAXWELL EQUATIONS 14 1 2 GAUGE TRANSFORMATIONS 14 2 THE COULOMB GAUGE 14 3 THE LAGRANGIAN DENSITY FOR THE ELECTROMAGNETIC FIELD 14 4 THE FREE ELECTROMAGNATIC FIELD AND ITS QUANTIZATION 14 5 CALCULATION OF THE PHOTON PROPAGATOR 15 INTERACTING FIELDS, QUANTUM ELECTRODYNAMICS 15 1 LAGRANGIANS, INTERACTING FIELDS 15 1 1 NONLINEAR LAGRANGIANS 15 1 2 FERMIONS IN AN EXTERNAL FIELD 15 1 3 INTERACTION OF ELECTRONS WITH THE RADIATION FIELD: QUANTUM ELECTRODYNAMICS (QED) 15 2 THE INTERACTION REPRESENTATION, PERTURBATION THEORY 15 2 1 THE INTERACTION REPRESENTATION (DIRAC REPRESENTATION) 15 2 2 PERTURBATION THEORY 15 3 THE S MATRIX 15 3 1 GENERAL FORMULATION 15 3 2 SIMPLE TRANSITIONS ?15 4 WICK’S THEOREM 15 5 SIMPLE SCATTERING PROCESSES, FEYNMAN DIAGRAMS 15 5 1 THE FIRST-ORDER TERM 15 5 2 MOTT SCATTERING 15 5 3 SECOND-ORDER PROCESSES 15 5 4 FEYNMAN RULES OF QUANTUM ELECTRODYNAMICS ?15 6 RADIATIVE CORRECTIONS 15 6 1 THE SELF-ENERGY OF THE ELECTRON 15 6 2 SELF-ENERGY OF THE PHOTON, VACUUM POLARIZATION 15 6 3 VERTEX CORRECTIONS 15 6 4 THE WARD IDENTITY AND CHARGE RENORMALIZATION 15 6 5 ANOMALOUS MAGNETIC MOMENT OF THE ELECTRON BIBLIOGRAPHY FOR PART III