This book gives a comprehensive account of local quantum physics, understood as the synthesis of quantum theory with the principle of locality. Centered on the algebraic approach it describes both the physical concepts and the mathematical structures, and their consequences. These include the emergence of the particle picture, general collision theory covering the cases of massless particles and infraparticles, the analysis of possible charge structures and exchange symmetries, including braid group statistics. Thermal states of an unbounded medium and local equilibrium are discussed in…mehr
This book gives a comprehensive account of local quantum physics, understood as the synthesis of quantum theory with the principle of locality. Centered on the algebraic approach it describes both the physical concepts and the mathematical structures, and their consequences. These include the emergence of the particle picture, general collision theory covering the cases of massless particles and infraparticles, the analysis of possible charge structures and exchange symmetries, including braid group statistics. Thermal states of an unbounded medium and local equilibrium are discussed in detail. The author takes care both to describe the ideas and to give a critical assessment of future perspectives. A special chapter deals with formalism and interpretation of quantum theory.The new edition provided the opportunity of adding a new chapter entitled "Principles and Lessons of Quantum Physics". It was a tempting challenge to try to sharpen the points at issue in the long lasting debate on the Copenhagen Spirit, to assess the significance of various arguments from our present vantage point, seventy years after the advent of quantum theory, where, after ali, some problems appear in a different light. It includes a section on the assumptions leading to the specific mathematical formalism of quantum theory and a section entitled "The evolutionary picture" describing my personal conclusions. Alto gether the discussion suggests that the conventional language is too narrow and that neither the mathematical nor the conceptual structure are built for eter nity. Future theories will demand radical changes though not in the direction of a return to determinism. Essential lessons taught by Bohr will persist. This chapter is essentially self-contained. Some new material has been added in the last chapter. It concerns the char acterization of specific theories within the general frame and recent progress in quantum field theory on curved space-time manifolds. A few pages on renor malization have been added in Chapter II and some effort has been invested in the search for mistakes and unclear passages in the first edition. The central objective of the book, expressed in the title "Local Quantum Physics", is the synthesis between special relativity and quantum theory to gether with a few other principles of general nature.
I. Background.- 1. Quantum Mechanics.- Basic concepts, mathematical structure, physical interpretation..- 2. The Principle of Locality in Classical Physics and the Relativity Theories.- Faraday's vision. Fields..- 2.1 Special relativity. Poincaré group. Lorentz group. Spinors. Conformal group..- 2.2 Maxwell theory..- 2.3 General relativity..- 3. Poincaré Invariant Quantum Theory.- 3.1 Geometric symmetries in quantum physics. Projective representations and the covering group..- 3.2 Wigner's analysis of irreducible, unitary representations of the Poincare group. 3.3 Single particle states. Spin..- 3.4 Many particle states: Bose-Fermi alternative, Fock space, creation operators. Separation of CM-motion..- 4. Action Principle.- Lagrangean. Double rôle of physical quantities. Peierls' direct definition of Poisson brackets. Relation between local conservation laws and symmetries..- 5. Basic Quantum Field Theory.- 5.1 Canonical quantization..- 5.2 Fields and particles..- 5.3 Free fields..- 5.4 The Maxwell-Dirac system. Gauge invariance..- 5.5 Processes..- II. General Quantum Field Theory.- 1. Mathematical Considerations and General Postulates.- 1.1 The representation problem..- 1.2 Wightman axioms..- 2. Hierarchies of Functions.- 2.1 Wightman functions, reconstruction theorem, analyticity in x-space..- 2.2 Truncated functions, clustering. Generating functionals and linked cluster theorem..- 2.3 Time ordered functions..- 2.4 Covariant perturbation theory, Feynman diagrams. Renormalization..- 2.5 Vertex functions and structure analysis..- 2.6 Retarded functions and analyticity in p-space..- 2.7 Schwinger functions and Osterwalder-Schrader theorem..- 3. Physical Interpretation in Terms of Particles.- 3.1 The particle picture: Asymptotic particle configurations and collision theory..- 3.2 Asymptotic fields. S-matrix..- 3.3 LSZ-formalism..- 4. General Collision Theory.- 4.1 Polynomial algebras of fields. Almost local operators..- 4.2 Construction of asymptotic particle states..- 4.3. Coincidence arrangements of detectors..- 4.4 Generalized LSZ-formalism..- 5. Some Consequences of the Postulates.- 5.1 CPT-operator. Spin-statistics theorem. CPT-theorem..- 5.2 Analyticity of the S-matrix..- 5.3 Reeh-Schlieder theorem..- 5.4 Additivity of the energy-momentum-spectrum..- 5.5 Borchers classes..- III. Algebras of Local Observables and Fields.- 1. Review of the Perspective.- Characterization of the theory by a net of local algebras. Bounded operators. Unobservable fields, superselection rules and the net of abstract algebras of observables. Transcription of the basic postulates..- 2. Von Neumann Algebras. C -Algebras. W -Algebras.- 2.1 Algebras of bounded operators. Concrete C -algebras and von Neumann algebras. Isomorphisms. Reduction. Factors. Classification of factors..- 2.2 Abstract algebras and their representations. Abstract C -algebras. Relation between the C -norm and the spectrum. Positive linear forms and states. The GNS-construction. Folia of states. Intertwiners. Primary states and cluster property. Purification. W -algebras..- 3. The Net of Algebras of Local Observables.- 3.1 Smoothness and integration. Local definiteness and local normality..- 3.2 Symmetries and symmetry breaking. Vacuum states. The spectral ideals..- 3.3 Summary of the structure..- 4. The Vacuum Sector.- 4.1 The orthocomplemented lattice of causally complete regions..- 4.2 The net of von Neumann algebras in the vacuum representation..- IV. Charges, Global Gauge Groups and Exchange Symmetry.- 1. Charge Superselection Sectors.- "Strange statistics". Charges. Selection criteria for relevant sectors. The program and survey of results..- 2. The DHR-Analysis.- 2.1 Localized morphisms..- 2.2 Intertwiners and exchange symmetry ("Statistics")..- 2.3 Charge conjugation, statistics parameter..- 2.4 Covariant sectors and energy-momentum spectrum..- 2.5 Fields and collision theory..- 3. The Buchholz-Fredenhagen-Analysis.- 3.1 Localized 1-particle states..- 3.2 BF-topologica
From the reviews: "This book is by no means the summa of the field of algebraic quantum field theory." Mathematical Reviews "Indeed, both the expert in the field and the novice will enjoy Haag's insightful exposition of the basic physics behind the abstract mathematics, and his unique way of making complicated mathematical theorems plausible without getting bogged down in tedious details." - Physics Today
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