A UNIFIED GRAND TOUR OF THEORETICAL PHYSICS
CONTENTS INTRODUCTION: THE WAYS OF NATURE GEOMETRY THE SPECIAL AND GENERAL THEORIES OF RELATIVITY THE SPECIAL THEORY THE GENERAL THEORY SPACETIME AS A DIFFERENTIABLE MANIFOLD TOPOLOGY OF THE REAL LINE R AND OF RD DIFFERENTIABLE SPACETIME MANIFOLD SUMMARY AND EXAMPLES TENSORS EXTRA GEOMETRICAL STRUCTURES THE AF?NE CONNECTION GEODESICS THE RIEMANN CURVATURE TENSOR THE METRIC THE METRIC CONNECTION WHAT IS THE STRUCTURE OF OUR SPACETIME? CLASSICAL PHYSICS IN GALILEAN AND MINKOWSKI SPACETIMES THE ACTION PRINCIPLE IN GALILEAN SPACETIME SYMMETRIES AND CONSERVATION LAWS THE HAMILTONIAN POISSON BRACKETS AND TRANSLATION OPERATORS THE ACTION PRINCIPLE IN MINKOWSKI SPACETIME CLASSICAL ELECTRODYNAMICS GEOMETRY IN CLASSICAL PHYSICS MORE ON TENSORS DIFFERENTIAL FORMS, DUAL TENSORS AND MAXWELL’S EQUATIONS CON?GURATION SPACE AND ITS RELATIVES THE SYMPLECTIC GEOMETRY OF PHASE SPACE GENERAL RELATIVITY AND GRAVITATION THE PRINCIPLE OF EQUIVALENCE GRAVITATIONAL FORCES THE FIELD EQUATIONS OF GENERAL RELATIVITY THE GRAVITATIONAL FIELD OF A SPHERICAL BODY THE SCHWARZSCHILD SOLUTION TIME NEAR A MASSIVE BODY DISTANCES NEAR A MASSIVE BODY PARTICLE TRAJECTORIES NEAR A MASSIVE BODY BLACK AND WHITE HOLES QUANTUM THEORY WAVE MECHANICS THE HILBERT SPACE OF STATE VECTORS OPERATORS AND OBSERVABLE QUANTITIES SPACETIME TRANSLATIONS AND THE PROPERTIES OF OPERATORS QUANTIZATION OF A CLASSICAL SYSTEM AN EXAMPLE: THE ONE-DIMENSIONAL HARMONIC OSCILLATOR SECOND QUANTIZATION AND QUANTUM FIELD THEORY THE OCCUPATION-NUMBER REPRESENTATION FIELD OPERATORS AND OBSERVABLES EQUATION OF MOTION AND LAGRANGIAN FORMALISM FOR FIELD OPERATORS SECOND QUANTIZATION FOR FERMIONS RELATIVISTIC WAVE EQUATIONS AND FIELD THEORIES THE KLEIN–GORDON EQUATION SCALAR FIELD THEORY FOR FREE PARTICLES THE DIRAC EQUATION AND SPIN 2 PARTICLES THE DIRAC EQUATION LORENTZ COVARIANCE AND SPIN SOME PROPERTIES OF THE ? MATRICES CONJUGATE WAVEFUNCTION AND THE DIRAC ACTION PROBABILITY CURRENT AND BILINEAR COVARIANTS PLANE-WAVE SOLUTIONS MASSLESS SPIN 2 PARTICLES SPINOR FIELD THEORY WEYL AND MAJORANA SPINORS PARTICLES OF SPIN 1 AND PHOTONS AND MASSIVE SPIN-1 PARTICLES GRAVITONS WAVE EQUATIONS IN CURVED SPACETIME FORCES, CONNECTIONS AND GAUGE FIELDS ELECTROMAGNETISM NON-ABELIAN GAUGE THEORIES NON-ABELIAN THEORIES AND ELECTROMAGNETISM RELEVANCE OF NON-ABELIAN THEORIES TO PHYSICS THE THEORY OF KALUZA AND KLEIN INTERACTING RELATIVISTIC FIELD THEORIES ASYMPTOTIC STATES AND THE SCATTERING OPERATOR REDUCTION FORMULAE PATH INTEGRALS PATH INTEGRALS IN NON-RELATIVISTIC QUANTUM MECHANICS FUNCTIONAL INTEGRALS IN QUANTUM ?ELD THEORY PERTURBATION THEORY QUANTIZATION OF GAUGE FIELDS RENORMALIZATION QUANTUM ELECTRODYNAMICS THE COULOMB POTENTIAL VACUUM POLARIZATION THE LAMB SHIFT THE RUNNING COUPLING CONSTANT ANOMALOUS MAGNETIC MOMENTS 10 EQUILIBRIUM STATISTICAL MECHANICS 10 1 ERGODIC THEORY AND THE MICROCANONICAL ENSEMBLE 10 2 THE CANONICAL ENSEMBLE 10 3 THE GRAND CANONICAL ENSEMBLE 10 4 RELATION BETWEEN STATISTICAL MECHANICS AND THERMODYNAMICS 10 5 QUANTUM STATISTICAL MECHANICS 10 6 FIELD THEORIES AT FINITE TEMPERATURE 10 7 BLACK BODY RADIATION 10 8 THE CLASSICAL LATTICE GAS 10 9 ANALOGIES BETWEEN FIELD THEORY AND STATISTICAL MECHANICS 11 PHASE TRANSITIONS 11 1 BOSE–EINSTEIN CONDENSATION 11 2 CRITICAL POINTS IN FLUIDS AND MAGNETS 11 3 THE ISING MODEL AND ITS APPROXIMATION BY A FIELD THEORY 11 4 ORDER, DISORDER AND SPONTANEOUS SYMMETRY BREAKING 11 5 THE GINZBURG–LANDAU THEORY 11 6 THE RENORMALIZATION GROUP 11 7 THE GINZBURG–LANDAU THEORY OF SUPERCONDUCTORS 11 7 1 SPONTANEOUS BREAKING OF CONTINUOUS SYMMETRIES 11 7 2 MAGNETIC EFFECTS IN SUPERCONDUCTORS 11 7 3 THE HIGGS MECHANISM 12 UNI?ED GAUGE THEORIES OF THE FUNDAMENTAL INTERACTIONS 12 1 THE WEAK INTERACTION 12 2 THE GLASHOW–WEINBERG–SALAM MODEL FOR LEPTONS 12 3 PHYSICAL IMPLICATIONS OF THE MODEL FOR LEPTONS 12 4 HADRONIC PARTICLES IN THE ELECTROWEAK THEORY 12 4 1 QUARKS 12 4 2 QUARKS IN THE ELECTROWEAK THEORY 12 5 COLOUR AND QUANTUM CHROMODYNAMICS 12 6 GRAND UNI?ED THEORIES 12 7 SUPERSYMMETRY 12 7 1 THE WESS–ZUMINO MODEL 12 7 2 SUPER?ELDS 12 7 3 SPONTANEOUS SUPERSYMMETRY BREAKING 12 7 4 THE SUPERSYMMETRY ALGEBRA 12 7 5 SUPERSYMMETRIC GAUGE THEORIES AND SUPERGRAVITY 12 7 6 SOME ALGEBRAIC DETAILS 13 SOLITONS AND SO ON 13 1 DOMAIN WALLS AND KINKS 13 2 THE SINE–GORDON SOLITONS 13 3 VORTICES AND STRINGS 13 4 MAGNETIC MONOPOLES 14 THE EARLY UNIVERSE 14 1 THE ROBERTSON–WALKER METRIC 14 2 THE FRIEDMANN–LEMAˆITRE MODELS 14 3 MATTER, RADIATION AND THE AGE OF THE UNIVERSE 14 4 THE FAIRLY EARLY UNIVERSE 14 5 NUCLEOSYNTHESIS 14 6 RECOMBINATION AND THE HORIZON PROBLEM 14 7 THE FLATNESS PROBLEM 14 8 THE VERY EARLY UNIVERSE 15 AN INTRODUCTION TO STRING THEORY 15 1 THE RELATIVISTIC POINT PARTICLE 15 2 THE FREE CLASSICAL STRING 15 2 1 THE STRING ACTION 15 2 2 WEYL INVARIANCE AND GAUGE ?XING 15 2 3 THE EUCLIDEAN WORLDSHEET AND CONFORMAL INVARIANCE 15 2 4 MODE EXPANSIONS 15 2 5 A USEFUL TRANSFORMATION 15 3 QUANTIZATION OF THE FREE BOSONIC STRING 15 3 1 THE QUANTUM VIRASORO ALGEBRA 15 3 2 QUANTUM GAUGE ?XING 15 3 3 THE CRITICAL SPACETIME DIMENSION 15 3 4 THE GHOST HILBERT SPACE 15 3 5 THE BRST COHOMOLOGY 15 4 PHYSICS OF THE FREE BOSONIC STRING 15 4 1 THE MASS SPECTRUM 15 4 2 VERTEX OPERATORS 15 4 3 STRINGS AND QUANTUM GRAVITY 15 5 FURTHER DEVELOPMENTS 15 5 1 STRING INTERACTIONS 15 5 2 SUPERSTRINGS 15 5 3 THE RAMI?CATIONS OF COMPACTI?CATION 15 6 THE LAST WORD? SOME SNAPSHOTS OF THE TOUR