Local quantum physics: fields, particles, algebras

LOCAL QUANTUM PHYSICS: FIELDS, PARTICLES, ALGEBRAS, 2ND ED.......Page 1
Title Page......Page 3
Copyright Page......Page 4
Dedication......Page 6
Preface to the Second Edition......Page 8
From the Preface to the First Edition......Page 9
Organization of the Book......Page 10
Contents......Page 12
I.1 Quantum Mechanics......Page 18
I.2 The Principle of Locality in Classical Physics and the Relativity Theories......Page 24
I.2.1 Special Relativity, Poincaré Group, Lorentz Group, Spinors, Conformal Group......Page 25
I.2.2 Maxwell Theory......Page 34
I.2.3 General Relativity......Page 38
I.3.1 Geometric Symmetries in Quantum Physics. Projective Representations and the Covering Group......Page 42
I.3.2 Wigner\'s Analysis of Irreducible Unitary Representations of the Poincaré Group......Page 45
I.3.3 Single Particle States. Spin......Page 48
I.3.4 Many Particle States......Page 52
I.4 Action Principle......Page 56
I.5.1 Canonical Quantization......Page 59
I.5.2 Fields and Particles......Page 61
I.5.3 Free Fields......Page 63
I.5.4 The Maxwell–Dirac System......Page 65
I.5.5 Processes......Page 68
II.1.1 The Representation Problem......Page 70
B. Fields......Page 73
E. Causality......Page 74
II.2 Hierarchies of Functions......Page 75
II.2.1 Wightman Functions, Reconstruction Theorem, Analyticity in x-Space......Page 76
II.2.2 Truncated Functions. Clustering......Page 78
II.2.3 Time Ordered Functions......Page 81
II.2.4 Covariant Perturbation Theory. Feynman Diagrams. Renormalization......Page 82
II.2.5 Vertex Functions and Structure Analysis......Page 88
II.2.7 Schwinger Functions and Osterwalder–Schrader Theorem......Page 90
II.3.1 The Particle Picture......Page 92
II.3.2 Asymptotic Fields. S-Matrix......Page 97
II.3.3 LSZ-Formalism......Page 98
II.4.1 Polynomial Algebras of Fields. Almost Local Operators......Page 101
II.4.2 Construction of Asymptotic Particle States......Page 104
II.4.3 Coincidence Arrangements of Detectors......Page 109
II.4.4 Generalized LSZ-Formalism......Page 111
II.5.1 CPT-Operator. Spin-Statistics-Theorem......Page 113
II.5.2 Analyticity of the S-Matrix......Page 117
II.5.3 The Theorem of Reeh and Schlieder......Page 118
II.5.4 Additivity of the Energy-Momentum Spectrum......Page 119
II.5.5 Borchers Classes......Page 121
III.1 Review of the Perspective......Page 122
III.2.1 Algebras of Bounded Operators......Page 129
III.2.2 Abstract Algebras and Their Representations......Page 135
III.3 The Net of Algebras of Observables......Page 145
III.3.1 Smoothness and Integration. Local Definiteness and Local Normality......Page 146
III.3.2 Symmetries and Symmetry Breaking. Vacuum States......Page 149
III.3.3 Summary of the Structure......Page 158
III.4.1 The Lattice of Causally Complete Regions......Page 160
III.4.2 The von Neumann Rings in the Vacuum Sector......Page 161
IV.1 Charge Superselection Sectors......Page 166
IV.2.1 Localized Morphisms......Page 173
IV.2.2 Intertwiners and Exchange Symmetry (Statistics)......Page 176
IV.2.3 Charge Conjugation, Statistics Parameter......Page 184
IV.2.4 Covariant Sectors and Energy-Momentum Spectrum......Page 188
IV.2.5 Fields and Collision Theory......Page 189
IV.3.1 Localized Single Particle States......Page 191
IV.3.2 BF Topological Charges......Page 194
IV.3.3 Composition of Sectors and Exchange Symmetry......Page 199
IV.3.4 Charge Conjugation and Absence of Infinite Statistics......Page 200
IV.4 Global Gauge Group and Charge Carrying Fields......Page 201
IV.5 Low Dimensional Space-Time and Braid Group Statistics......Page 209
V.1.1 Introduction......Page 216
V.1.2 Equivalence of KMS-Condition and Gibbs Canonical Ensembles for Finite V......Page 220
V.1.3 The Arguments for Gibbs Ensembles......Page 221
V.1.4 The Representation Induced by a KMS-State......Page 224
V.1.5 Phases, Symmetry Breaking and Decomposition of KMS-States......Page 229
V.1.6 Extremality and Autocorrelation Inequalities......Page 231
V.2.1 The Tomita–Takesaki Theorem......Page 233
V.2.2 Vector Representatives of States. Convex Cones in H......Page 236
V.2.3 Relative Modular Operators and Radon–Nikodym Derivatives......Page 239
V.2.4 Classification of Factors......Page 241
V.3.2 Stability......Page 244
V.3.3 Passivity......Page 252
V.3.4 Chemical Potential......Page 256
V.4.1 The Bisognano–Wichmann Theorem......Page 262
V.4.2 Conformal Invariance and the Theorem of Hislop and Longo......Page 266
V.5.1 Introduction......Page 271
V.5.2 Nuclearity and Split Property......Page 275
V.5.3 Open Subsystems......Page 280
V.5.4 Modular Nuclearity......Page 282
V.6 The Universal Type of Local Algebras......Page 284
VI.1.1 Generalities......Page 288
VI.1.2 Asymptotic Particle Configurations......Page 292
VI.2.1 Particles and Infraparticles......Page 296
VI.2.2 Single Particle Weights and Their Decomposition......Page 299
VI.2.3 Further Remarks on the Particle Picture and Its Completeness......Page 304
VI.3 The Physical State Space of Quantum Electrodynamics......Page 306
Introduction......Page 310
VII.1 The Copenhagen Spirit. Criticisms, Elaborations......Page 311
VII.2 The Mathematical Formalism......Page 321
VII.3 The Evolutionary Picture......Page 326
VIII.1 Algebraic Approach vs. Euclidean Quantum Field Theory......Page 340
VIII.2 Supersymmetry......Page 346
VIII.3.1 Introduction......Page 349
VIII.3.2 Quantum Field Theory in Curved Space-Time......Page 350
VIII.3.3 Hawking Temperature and Hawking Radiation......Page 358
VIII.3.4 A Few Remarks on Quantum Gravity......Page 364
Bibliography......Page 366
Author Index and References......Page 372
Subject Index......Page 404
Back Cover......Page 408