Local quantum physics: fields, particles, algebras
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin u.a.
Springer
1993
|
| Edition: | Corr. 2. print. |
| Series: | Texts and monographs in physics
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIV, 356 S. graph. Darst. |
| ISBN: | 3540536108 0387536108 |
Staff View
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Record in the Search Index
| _version_ | 1804120757653995520 |
|---|---|
| adam_text | Rudolf Haag
Local
Quantum Physics
Fields, Particles, Algebras
With 15 Figures
Springer-Verlag
Berlin Heidelberg New York
London Paris Tokyo
Hong Kong Barcelona
Budapest
Contents
I Background 1
1 Quantum Mechanics 1
Basic concepts, mathematical structure, physical interpretation
2 The Principle of Locality in Classical Physics
and the Relativity Theories 9
Faraday s vision Fields 2 1 Special relativity Poincare group Lorentz group
Spinors Conformal group 2 2 Maxwell theory 2 3 General relativity
3 Poincare Invariant Quantum Theory 27
3 1 Geometric symmetries in quantum physics Projective representations and
the covering group 3 2 Wigner s analysis of irreducible, unitary representa-
tions 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 40
Lagrangean Double role of physical quantities Peierls direct definition of Pois-
son brackets Relation between local conservation laws and symmetries
5 Basic Quantum Field Theory 44
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 55
1 Mathematical Considerations and General Postulates 55
1 1 The representation problem 1 2 Wightman axioms
2 Hierarchies of Functions 60
2 1 Wightman functions, reconstruction theorem, analyticity in a space
2 2 Truncated functions, clustering Generating functional and linked cluster
XII Contents
theorem 2 3 Time ordered functions 2 4 Covariant perturbation theory, Feyn-
man 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 75
3 1 The particle picture: Asymptotic particle configurations and collision the-
ory 3 2 Asymptotic fields S-matrix 3 3 LSZ-formalism
4 General Collision Theory 83
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 96
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 105
1 Review of the Perspective 105
Characterization of the theory by a net of local algebras Bounded operators
Unobservable fields, superselection rules and the net of abstract algebras of ob-
servables Transcription of the basic postulates
2 Von Neumann Algebras C*-Algebras W*-Algebras 112
2 1 Algebras of bounded operators Concrete C*-algebras and von Neumann
algebras Isomorphisms Reduction Factors Classification of factors 2 2 Ab-
stract algebras and their representations Abstract C*-algebras Relation be-
tween the C -norm and the spectrum Positive linear forms and states The
GNS-construction Folia of states Intertwiners Primary states and cluster prop-
erty Purification W*-algebras
3 The Net of Algebras of Local Observables 129
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 143
4 1 The orthocomplemented lattice of causally complete regions 4 2 The net of
von Neumann algebras in the vacuum representation
Contents XIII
IV Charges, Global Gauge Groups
and Exchange Symmetry 149
1 Charge Superselection Sectors 149
Strange statistics Charges Selection criteria for relevant sectors The pro-
gram and survey of results
2 The DHR-Analysis 156
2 1 Localized morphisms 2 2 Intertwiners and exchange symmetry (Statis-
tics) 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 174
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 in-
finite statistics
4 Global Gauge Group and Charge Carrying Fields 184
The Abelian case Endomorphisms and non-Abelian gauge group DR-categories
Implementation of endomorphisms and the embedding theorem
5 Low Dimensional Space-Time and Braid Group Statistics 192
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 199
1 Gibbs Ensembles, Thermodynamic Limit, KMS-Condition 199
1 1 Introduction 1 2 Equivalence of KMS-condition to Gibbs ensembles for fi-
nite volume 1 3 The arguments for Gibbs ensembles 1 4 The representation
induced by a KMS-state 1 5 Phases, symmetry breaking and the decomposi-
tion of KMS-states 1 6 Variational principles and autocorrelation inequalities
2 Modular Automorphisms and Modular Conjugation 216
2 1 The Tomita-Takesaki theorem 2 2 Vector representatives of states Convex
cones in Ti 2 3 Relative modular operators and Radon-Nikodym derivatives
2 4 Classification of factors
3 Direct Characterization of Equilibrium States 226
3 1 Introduction 3 2 Stability 3 3 Passivity 3 4 Chemical potential
4 Modular Automorphisms of Local Algebras 244
4 1 The Bisognano-Wichmann theorem 4 2 Conformal invariance and the
theorem of Hislop and Longo
XIV Contents
5 Phase Space, Nuclearity, Split Property, Local Equilibrium 253
5 1 Introduction 5 2 Nuclearity and split property 5 3 Open subsystems
5 4 Modular nuclearity
6 The Universal Type of Local Algebras 267
V I Part ic les Completeness of the Partic le Picture 271
1 Detectors, Coincidence Arrangements, Cross Sections 271
1 1 Generalities 1 2 Asymptotic particle configurations Buchholz s strategy
2 The Particle Content 279
2 1 Particles and infraparticles 2 2 Single particle weights and their decompo-
sition 2 3 Remarks on the particle picture and its completeness
3 The Physical State Space of Quantum Electrodynamics 289
VII Retrospective and Outlook 297
1 Algebraic Approach vs Euclidean Quantum Field Theory 297
2 Supersymmetry 300
3 The Challenge from General Relativity 303
3 1 Introduction 3 2 Quantum field theory in curved space-time 3 3 Haw-
king temperature and Hawking radiation 34A few remarks on quantum gra-
vity
Bibliography 319
Author Index and References 323
Subject Index 353
|
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| discipline | Physik |
| edition | Corr. 2. print. |
| format | Book |
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| id | DE-604.BV006495579 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T16:47:10Z |
| institution | BVB |
| isbn | 3540536108 0387536108 |
| language | English |
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| physical | XIV, 356 S. graph. Darst. |
| publishDate | 1993 |
| publishDateSearch | 1993 |
| publishDateSort | 1993 |
| publisher | Springer |
| record_format | marc |
| series2 | Texts and monographs in physics |
| spelling | Haag, Rudolf 1922-2016 Verfasser (DE-588)124520987 aut Local quantum physics fields, particles, algebras Rudolf Haag Corr. 2. print. Berlin u.a. Springer 1993 XIV, 356 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Texts and monographs in physics Quantentheorie Quantum field theory Quantum theory Quantenfeldtheorie (DE-588)4047984-5 gnd rswk-swf Lokalisation (DE-588)4195351-4 gnd rswk-swf Algebraische Methode (DE-588)4141841-4 gnd rswk-swf Quantenphysik (DE-588)4266670-3 gnd rswk-swf Algebra (DE-588)4001156-2 gnd rswk-swf Quantenmechanik (DE-588)4047989-4 gnd rswk-swf Quantenfeldtheorie (DE-588)4047984-5 s Algebraische Methode (DE-588)4141841-4 s DE-604 Quantenmechanik (DE-588)4047989-4 s Lokalisation (DE-588)4195351-4 s Algebra (DE-588)4001156-2 s 1\p DE-604 2\p DE-604 Quantenphysik (DE-588)4266670-3 s 3\p DE-604 HEBIS Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=004130721&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Haag, Rudolf 1922-2016 Local quantum physics fields, particles, algebras Quantentheorie Quantum field theory Quantum theory Quantenfeldtheorie (DE-588)4047984-5 gnd Lokalisation (DE-588)4195351-4 gnd Algebraische Methode (DE-588)4141841-4 gnd Quantenphysik (DE-588)4266670-3 gnd Algebra (DE-588)4001156-2 gnd Quantenmechanik (DE-588)4047989-4 gnd |
| subject_GND | (DE-588)4047984-5 (DE-588)4195351-4 (DE-588)4141841-4 (DE-588)4266670-3 (DE-588)4001156-2 (DE-588)4047989-4 |
| title | Local quantum physics fields, particles, algebras |
| title_auth | Local quantum physics fields, particles, algebras |
| title_exact_search | Local quantum physics fields, particles, algebras |
| title_full | Local quantum physics fields, particles, algebras Rudolf Haag |
| title_fullStr | Local quantum physics fields, particles, algebras Rudolf Haag |
| title_full_unstemmed | Local quantum physics fields, particles, algebras Rudolf Haag |
| title_short | Local quantum physics |
| title_sort | local quantum physics fields particles algebras |
| title_sub | fields, particles, algebras |
| topic | Quantentheorie Quantum field theory Quantum theory Quantenfeldtheorie (DE-588)4047984-5 gnd Lokalisation (DE-588)4195351-4 gnd Algebraische Methode (DE-588)4141841-4 gnd Quantenphysik (DE-588)4266670-3 gnd Algebra (DE-588)4001156-2 gnd Quantenmechanik (DE-588)4047989-4 gnd |
| topic_facet | Quantentheorie Quantum field theory Quantum theory Quantenfeldtheorie Lokalisation Algebraische Methode Quantenphysik Algebra Quantenmechanik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=004130721&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT haagrudolf localquantumphysicsfieldsparticlesalgebras |