Local Quantum Physics: Fields, Particles, Algebras (theoretical And Mathematical Physics)

Four years aga Walter Thirring suggested to me that it would be desirable to have a book describing recent results of the "algebraic approach" to quantum field theory and statistical mechanics. After long deliberations with my younger colleagues I decided to write a book but to enlarge the topic, the guiding line be­ ing expressed in the title "Local Quantum Physics". In essence this concerns the synthesis between special relativity and our understanding of quantum physics, together with a few other principles of a general nature. The algebraic approach, that is the characterization of the theory by a net of algebras of local observ­ ables, provides a concise language for this and an efficient tool for the study of the anatomy of the theory and of the relevance of various parts to qualita­ tive physical consequences. It is introduced in Chapter III. In compliance with the original suggestion its main results of more recent vintage are described in Chapters IV to VI. The first two chapters serve to place this material into context and make the book reasonably self contained. There is a rough tem­ poral order. Thus Chapter I briefly describes the pillars of the theory existing before 1950. Chapter II deals with progress in understanding and techniques in quantum field theory, achieved for the most part in the fifties and early sixties Front Matter....Pages I-XIV Quantum Mechanics....Pages 1-9 The Principle of Locality in Classical Physics and the Relativity Theories....Pages 9-27 Poincaré Invariant Quantum Theory....Pages 27-40 Action Principle....Pages 40-44 Basic Quantum Field Theory....Pages 44-53 Mathematical Considerations and General Postulates....Pages 55-60 Hierarchies of Functions....Pages 60-75 Physical Interpretation in Terms of Particles....Pages 75-83 General Collision Theory....Pages 83-95 Some Consequences of the Postulates....Pages 96-104 Review of the Perspective....Pages 105-112 Von Neumann Algebras. C*-Algebras. W*-Algebras....Pages 112-129 The Net of Algebras of Observables....Pages 129-143 The Vacuum Sector....Pages 143-147 Charge Superselection Sectors....Pages 149-156 The DHR-Analysis....Pages 156-174 The Buchholz-Fredenhagen (BF)-Analysis....Pages 174-184 Global Gauge Group and Charge Carrying Fields....Pages 184-192 Low Dimensional Space-Time and Braid Group Statistics....Pages 192-197 Gibbs Ensembles, Thermodynamic Limit, KMS-Condition....Pages 199-216 Modular Automorphisms and Modular Conjugation....Pages 216-226 Direct Characterization of Equilibrium States....Pages 226-244 Modular Automorphisms of Local Algebras....Pages 244-253 Phase Space, Nuclearity, Split Property, Local Equilibrium....Pages 253-266 The Universal Type of Local Algebras....Pages 267-269 Detectors, Coincidence Arrangements, Cross Sections....Pages 271-278 The Particle Content....Pages 279-289 The Physical State Space of Quantum Electrodynamics....Pages 289-295 Algebraic Approach vs. Euclidean Quantum Field Theory....Pages 297-300 Supersymmetry....Pages 300-303 The Challenge from General Relativity....Pages 303-318 Back Matter....Pages 319-356