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.
Recenzijas
"Indeed, both the expert in the field and the novice will enjoy Haags insightful exposition... This (superb) book is bound to occupy a place on a par with other classics in the mathematical physics literature." Physics Today "...enjoyable reading to anybody interested in the development of fundamental physical theories." Zentralblatt f. Mathematik
I. Background.-
1. Quantum Mechanics.- Basic concepts, mathematical
structure, physical interpretation..-
2. The Principle of Locality in
Classical Physics and the Relativity Theories.- Faradays 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 Wigners 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 rōle 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-topological charges..- 3.3 Composition of sectors
and exchange symmetry..- 3.4 Charge conjugation and the absence of infinite
statistics..-
4. Global Gauge Group and Charge Carrying Fields.-
Implementation of endomorphisms. Charges with d =
1. Endomorphisms and non
Abelian gauge group. DR categories and the embedding theorem..-
5. Low
Dimensional Space-Time and Braid Group Statistics.- Statistics operator and
braid group representations. The 2+1-dimensional case with BF-charges.
Statistics parameter and Jones index..- V. Thermal States and Modular
Automorphisms.-
1. Gibbs Ensembles, Thermodynamic Limit, KMS-Condition.- 1.1
Introduction..- 1.2 Equivalence of KMS-condition to Gibbs ensembles for
finite volume..- 1.3 The arguments for Gibbs ensembles..- 1.4 The
representation induced by a KMS-state..- 1.5 Phases, symmetry breaking and
the decomposition of KMS-states..- 1.6 Variational principles and
autocorrelation inequalities..-
2. Modular Automorphisms and Modular
Conjugation.- 2.1 The Tomita-Takesaki theorem..- 2.2 Vector representatives
of states. Convex cones in H..- 2.3 Relative modular operators and
Radon-Nikodym derivatives..- 2.4 Classification of factors..-
3. Direct
Characterization of Equilibrium States.- 3.1 Introduction..- 3.2 Stability..-
3.3 Passivity..- 3.4 Chemical potential..-
4. Modular Automorphisms of Local
Algebras.- 4.1 The Bisognano-Wichmann theorem..- 4.2 Conformal invariance and
the theorem of Hislop and Longo..-
5. Phase Space, Nuclearity, Split
Property, Local Equilibrium.- 5.1 Introduction..- 5.2 Nuclearity and split
property..- 5.3 Open subsystems..- 5.4 Modular nuclearity..-
6. The Universal
Type of Local Algebras.- VI. Particles. Completeness of the Particle
Picture.-
1. Detectors, Coincidence Arrangements, Cross Sections.- 1.1
Generalities..- 1.2 Asymptotic particle configurations. Buchholzs
strategy..-
2. The Particle Content.- 2.1 Particles and infraparticles..- 2.2
Single particle weights and their decomposition..- 2.3 Remarks on the
particle picture and its completeness..-
3. The Physical State Space of
Quantum Electrodynamics.- VII. Principles and Lessons of Quantum Physics. A
Review of Interpretations, Mathematical Formalism and Perspectives.-
1. The
Copenhagen Spirit. Criticisms, Elaborations.- Niels Bohrs epistemological
considerations. Realism. Physical systems and the division problem.
Persistent non-classical correlations. Collective coordinates, decoherence
and the classical approximation. Measurements. Correspondence and
quantization. Time reflection asymmetry of statistical conclusions..-
2. The
Mathematical Formalism.- Operational assumptions. Quantum Logic. Convex
cones..-
3. The Evolutionary Picture.- Events, causal links and their
attributes. Irreversibility. The EPR-effect. Ensembles vs. individuals.
Decisions. Comparison with standard procedure..- VIII. Retrospective and
Outlook.-
1. Algebraic Approach vs. Euclidean Quantum Field Theory.-
2.
Supersymmetry.-
3. The Challenge from General Relativity.- 3.1
Introduction..- 3.2 Quantum field theory in curved space-time..- 3.3 Hawking
temperature and Hawking radiation..- 3.4 A few remarks on quantum gravity..-
Author Index and References.
