A TEXT BOOK OF PHYSICS
CONTENTS INTRODUCTION PART I C0(X) AND B(H) CLASSICAL PHYSICS ON A ?NITE PHASE SPACE BASIC CONSTRUCTIONS OF PROBABILITY THEORY CLASSICAL OBSERVABLES AND STATES PURE STATES AND TRANSITION PROBABILITIES THE LOGIC OF CLASSICAL MECHANICS THE GNS-CONSTRUCTION FOR C(X) NOTES QUANTUM MECHANICS ON A ?NITE-DIMENSIONAL HILBERT SPACE QUANTUM PROBABILITY THEORY AND THE BORN RULE QUANTUM OBSERVABLES AND STATES PURE STATES IN QUANTUM MECHANICS THE GNS-CONSTRUCTION FOR MATRICES THE BORN RULE FROM BOHRI?CATION THE KADISON–SINGER PROBLEM GLEASON’S THEOREM PROOF OF GLEASON’S THEOREM EFFECTS AND BUSCH’S THEOREM 2 10 THE QUANTUM LOGIC OF BIRKHOFF AND VON NEUMANN CLASSICAL PHYSICS ON A GENERAL PHASE SPACE VECTOR ?ELDS AND THEIR ?OWS POISSON BRACKETS AND HAMILTONIAN VECTOR ?ELDS SYMMETRIES OF POISSON MANIFOLDS THE MOMENTUM MAP QUANTUM PHYSICS ON A GENERAL HILBERT SPACE THE BORN RULE FROM BOHRI?CATION (II) DENSITY OPERATORS AND NORMAL STATES THE KADISON–SINGER CONJECTURE GLEASON’S THEOREM IN ARBITRARY DIMENSION SYMMETRY IN QUANTUM MECHANICS SIX BASIC MATHEMATICAL STRUCTURES OF QUANTUM MECHANICS THE CASE H = C2 EQUIVALENCE BETWEEN THE SIX SYMMETRY THEOREMS PROOF OF JORDAN’S THEOREM PROOF OF WIGNER’S THEOREM SOME ABSTRACT REPRESENTATION THEORY REPRESENTATIONS OF LIE GROUPS AND LIE ALGEBRAS IRREDUCIBLE REPRESENTATIONS OF SU(2) IRREDUCIBLE REPRESENTATIONS OF COMPACT LIE GROUPS 5 10 SYMMETRY GROUPS AND PROJECTIVE REPRESENTATIONS 5 11 POSITION, MOMENTUM, AND FREE HAMILTONIAN 5 12 STONE’S THEOREM PART II BETWEEN C0(X) AND B(H) CLASSICAL MODELS OF QUANTUM MECHANICS FROM VON NEUMANN TO KOCHEN–SPECKER THE FREE WILL THEOREM PHILOSOPHICAL INTERMEZZO: FREE WILL IN THE FREE WILL THEOREM TECHNICAL INTERMEZZO: THE GHZ-THEOREM BELL’S THEOREMS THE COLBECK–RENNER THEOREM LIMITS: SMALL ¯H DEFORMATION QUANTIZATION QUANTIZATION AND INTERNAL SYMMETRY QUANTIZATION AND EXTERNAL SYMMETRY INTERMEZZO: THE BIG PICTURE INDUCED REPRESENTATIONS AND THE IMPRIMITIVITY THEOREM REPRESENTATIONS OF SEMI-DIRECT PRODUCTS QUANTIZATION AND PERMUTATION SYMMETRY LIMITS: LARGE N LARGE QUANTUM NUMBERS LARGE SYSTEMS QUANTUM DE FINETTI THEOREM FREQUENCY INTERPRETATION OF PROBABILITY AND BORN RULE QUANTUM SPIN SYSTEMS: QUASI-LOCAL C*-ALGEBRAS QUANTUM SPIN SYSTEMS: BUNDLES OF C*-ALGEBRAS SYMMETRY IN ALGEBRAIC QUANTUM THEORY SYMMETRIES OF C*-ALGEBRAS AND HAMHALTER’S THEOREM UNITARY IMPLEMENTABILITY OF SYMMETRIES MOTION IN SPACE AND IN TIME GROUND STATES OF QUANTUM SYSTEMS GROUND STATES AND EQUILIBRIUM STATES OF CLASSICAL SPIN SYSTEMS EQUILIBRIUM (KMS) STATES OF QUANTUM SYSTEMS SPONTANEOUS SYMMETRY BREAKING 10 1 SPONTANEOUS SYMMETRY BREAKING: THE DOUBLE WELL 10 2 SPONTANEOUS SYMMETRY BREAKING: THE ?EA 10 3 SPONTANEOUS SYMMETRY BREAKING IN QUANTUM SPIN SYSTEMS 10 4 SPONTANEOUS SYMMETRY BREAKING FOR SHORT-RANGE FORCES 10 5 GROUND STATE(S) OF THE QUANTUM ISING CHAIN 10 6 EXACT SOLUTION OF THE QUANTUM ISING CHAIN: N < ? 10 7 EXACT SOLUTION OF THE QUANTUM ISING CHAIN: N = ? 10 8 SPONTANEOUS SYMMETRY BREAKING IN MEAN-?ELD THEORIES 10 9 THE GOLDSTONE THEOREM 10 10 THE HIGGS MECHANISM THE MEASUREMENT PROBLEM 11 1 THE RISE OF ORTHODOXY 11 2 THE RISE OF MODERNITY: SWISS APPROACH AND DECOHERENCE 11 3 INSOLUBILITY THEOREMS 11 4 THE FLEA ON SCHR¨ODINGER’S CAT TOPOS THEORY AND QUANTUM LOGIC 12 1 C*-ALGEBRAS IN A TOPOS 12 2 THE GELFAND SPECTRUM IN CONSTRUCTIVE MATHEMATICS 12 3 INTERNAL GELFAND SPECTRUM AND INTUITIONISTIC QUANTUM LOGIC 12 4 INTERNAL GELFAND SPECTRUM FOR ARBITRARY C*-ALGEBRAS 12 5 “DASEINISATION” AND KOCHEN–SPECKER THEOREM