Quantum physics: a functional integral point of view
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York ; Berlin ; Heidelberg
Springer-Verlag
[1987]
|
| Edition: | Second edition |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Hier auch später erschienene, unveränderte Nachdrucke |
| Physical Description: | XXII, 535 Seiten Diagramme |
| ISBN: | 0387964762 3540964762 0387964770 3540964770 9780387964775 |
Staff View
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Record in the Search Index
| _version_ | 1804116749204848640 |
|---|---|
| adam_text | James Glimm
Arthur Jaffe
Quantum Physics
A Functional Integral Point of View
Second Edition
With 51 Illustrations
Springer-Verlag
New York Berlin Heidelberg
London Paris Tokyo
Contents
Preface v
Introduction - xiii
Conventions and Formulas xvii
List of Symbols xix
PART I An Introduction to Modern Physics
1 Quantum Theory 3
1 1 Overview - 3
1 2 Classical Mechanics 3
1 3 Quantum Mechanics 7
1 4 Interpretation 11
1 5 The Simple Harmonic Oscillator 12
1 6 Coulomb Potentials 20
J 7 The Hydrogen Atom •, 24
i 8 The Need for Quantum Fields 26
2 Classical Statistical Mechanics t 28
2 1 Introduction 28
2 2 The Classical Ensembles 30
2 3 The Ising Model and Lattice Fields 36
2 4 Series Expansion Methods 37
vii
viii Contents
3 The Feynman-Kac Formula 43
3 1 Wiener Measure 43
3 2 The Feynman-Kac Formula 47
3 3 Uniqueness of the Ground State 51
3 4 The Renormalized Feynman-Kac Formula 52
Correlation Inequalities and the Lee-Yang Theorem 56
4 1 Griffiths Inequalities 57
4 2 The Infinite Volume Limit 59
43C Inequalities 60
4 4 The FKG Inequality 64
4 5 The Lee-Yang Theorem 66
4 6 Analyticity of the Free Energy 69
4 7 Two Component Spins 71
Phase Transitions and Critical Points 73
5 1 Pure and Mixed Phases 73
5 2 The Mean Field Picture 75
5 3 Symmetry Breaking 78
5 4 The Droplet Model and Peierls Argument 81
5 5 Some Examples 86
Field Theory 90
6 1 Axioms 90
(i) Euclidean Axioms 90
(ii) Minkowski Space Axioms 97
6 2 The Fr,ee Field 100
6 3 Fock Space and Wick Ordering 106
6 4 Canonical Quantization 111
6 5 Fefmions 115
6 6 Interacting Fields 118
Appendix to Part I Hilbert Space Operators and
Functional Integrals _ 122
A 1 Bounded and Unbounded Operators on Hilbert Space 122
A 2 Positive Operators arid Bilinear Forms 129
A 3 Trace Class Operators and Nuclear Spaces 132
A 4 Gaussian Measures 136
A 5 The Lie Product Theorem 144
A 6 The Bochner-Minlos Theorem 148
A 7 Stochastic Integrals 150
A 8 Stochastic Differential Equations 153
Contents ix
PART II Function S,pace Integrals
7 Covariance Operator = Green s Function = Resolvent
Kernel = Euclidean Propagator = Fundamental Solution 159
7 1 Introduction 159
7 2 The Free Covariance 161
7 3 Periodic Boundary Conditions 163
7 4 Neumann Boundary Conditions 164
7 5 Dirichlet Boundary Conditions 165
7 6 Change of Boundary Conditions 166
7 7 Covariance Operator Inequalities 166
7 8 More General Dirichlet Data 168
7 9 Regularity of CB 173
7 10 Reflection Positivity 177
8 Quantization = Integration over Function Space 180
8 1 Introduction 180
8 2 Feynman Graphs 181
8 3 Wick Products 183
8 4 Formal Perturbation Theory 186
8 5 Estimates on Gaussian Integrals 188
8 6 Non-Gaussian Integrals, d=2 193
8 7 Finite Dimensional Approximations 199
9 Calculus and Renormalization on Function Space 202
91A Compilation of Useful Formulas 202
(i) Wick Product Identities 202
(ii) Gaussian Integrals 205
(iii) Integration by Parts 207
(iv) Limits of Measures 208
9 2 Infinitesimal Change of Covariance 210
9 3 Quadratic Perturbations 211
9 4 Perturbative Renormalization 215
9 5 Lattice Laplace and Covariance Operators 219
9 6 Lattice Approximation of P{4 )2 Measures 225
Estimates Independent of Dimension 229
10 1 Introduction , 229
10 2 Correlation Inequalities for P( / )2 Fields 229
10 3 Dirichlet or Neumann Monotonicity and Decoupling 231
10 4 Reflection Positivity 234
10 5 Multiple Reflections 236
10 6 Nonsymmetric Reflections 242
x Contents
11 Fields Without Cutoffs 249
11 1 Introduction 249
11 2 Monotone Convergence 249
11 3 Upper Bounds 251
12 Regularity and Axioms 255
12 1 Introduction 255
12 2 Integration by Parts 256
12 3 Nonlocal f J Bounds 259
12 4 Uniformity in the Volume 261
12 5 Regularity of the P(4 )2 Field 265
PART III The Physics of Quantum Fields
13 Scattering Theory: Time-Dependent Methods 273
13 1 Introduction 273
13 2 Multiparticle Potential Scattering 276
13 3 The Wave Operator for Quantum Fields 280
13 4 Wave Packets for Free Particles 283
13 5 The Haag-Ruelle Theory 285
14 Scattering Theory: Time-Independent Methods 292
14 1 Time-Ordered Correlation Functions 292
14 2 The S Matrix 295
14 3 Renormalization 296
14 4 The Bethe-Salpeter Kernel 300
15 The Magnetic Moment of the Electron 306
15 1 Classical Magnetic Moments 306
15 2 The Fine Structure of the Hydrogen Atom
and the Dirac Equation 308
15 3 The Dirac Theory 310
15 4 The Anomalous Moment 312
15 5 The Hyperfine Structure and the Lamb Shift
of the Hydrogen Atom • 315
16 Phase Transitions 316
16 1 Introduction 316
16 2 The Two Phase Region 320
Contents xi
16 3 Symmetry JLJnbroken, d=2 330
16 4 Symmetry Broken, 3 d 333
17 The 4 * Critical Point 339
17 1 Elementary Considerations 339
17 2 The Absence of Even Bound States 340
17 3 A Bound on the Coupling Constant Aphys 342
17 4 Existence of Particles and a Bound on dm2 /do 344
17 5 Existence of the f * Critical Point 345
17 6 Continuity of dfi at the Critical Point 348
17 7 Critical Exponents 349
17 8 t 1 351
17 9 The Scaling Limit 353
17 10 The Conjecture P6 0 354
18 The Cluster Expansion 356
18 1 Introduction 356
18 2 The Cluster Expansion 359
18 3 Clustering and Analyticity 365
18 4 Convergence: The Main Ideas 367
18 5 An Equation of Kirkwood-Salsburg Type 370
18 6 Covariance Operators 371
18 7 Convergence: The ProofrCompleted 376
19 From Path Integrals to Quantum Mechanics 379
19 1 Reconstruction of Quantum Fields 379
19 2 The Feynman-Kac Formula 382
19 3 Self-Adjoint Fields 384
19 4 Commutators 385
19 5 Lorentz Covariance 389
19 6 Locality 392
19 7 Uniqueness of the Vacuum 393
!0 The Polymer Expansion 398
20 1 Introduction 398
20 2 Activity Expansions and Connected Polymers 399
20 3 Convergence of the Polymer Expansion 405
20 4 The Tree Graph Decay of Correlations and the
Existence of the Free Energy 410
20 5 Polymer Expansion Examples
t 411
(i) The High Temperature Ising Model 412
(ii) The Weak Coupling of Euclidean Quantum Fields 413
(iii) Mayer Expansion of the Grand Canonical Partition
Function 416
(iv) Low Temperature Ising Model 416
xii Contents
21 Random Path Representations 419
21 1 Random Walks and the Laplacian 420
21 2 Local Stopping Times 421
21 3 Gaussian Integration by Parts 423
21 4 Non-Gaussian Integration by Parts 424
21 5 41* Correlation Inequalities 427
21 6 The j * Noninteraction Theorem 433
22 Constructive Gauge Theory and Phase Cell Localization 437
22 1 Introduction 437
22 2 Regularization and Lattice Approximations 442
22 3 Reflection Positivity of the Lattice Approximation 446
22 4 Phase Cell Localization and Exact Renormalization
Transformations 447
22 5 Infra-Red Behavior 451
22 6 Lattice Maxwell Theory—An Example of Renormalization 454
22 7 Nonabelian Gauge Models 457
23 Further Directions 460
23 1 The $ Model 460
23 2 Borel Summability 461
23/3 Euclidean Fermi Fields 462
23 4 Yukawa Interactions 463
23 5 Low Temperature Expansions and Phase Transitions 464
23 6 Debye Screening and the Sine-Gordon Transformation 465
23 7 Dipoles Don t Screen 468
23 8 Solitons 470
Bibliography 472
Index 529
|
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| id | DE-604.BV002289582 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T15:43:27Z |
| institution | BVB |
| isbn | 0387964762 3540964762 0387964770 3540964770 9780387964775 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-001504608 |
| oclc_num | 14966379 |
| open_access_boolean | |
| owner | DE-91G DE-BY-TUM DE-384 DE-19 DE-BY-UBM DE-355 DE-BY-UBR DE-29T DE-703 DE-634 DE-188 DE-83 |
| owner_facet | DE-91G DE-BY-TUM DE-384 DE-19 DE-BY-UBM DE-355 DE-BY-UBR DE-29T DE-703 DE-634 DE-188 DE-83 |
| physical | XXII, 535 Seiten Diagramme |
| publishDate | 1987 |
| publishDateSearch | 1987 |
| publishDateSort | 1987 |
| publisher | Springer-Verlag |
| record_format | marc |
| spelling | Glimm, James 1934- Verfasser (DE-588)140590005 aut Quantum physics a functional integral point of view James Glimm ; Arthur Jaffe Second edition New York ; Berlin ; Heidelberg Springer-Verlag [1987] XXII, 535 Seiten Diagramme txt rdacontent n rdamedia nc rdacarrier Hier auch später erschienene, unveränderte Nachdrucke Champs, Théorie quantique des Champs, Théorie quantique des ram Kwantummechanica gtt Kwantumveldentheorie gtt Physique statistique Physique statistique ram Quanta, Théorie des ram Statistische mechanica gtt Théorie quantique Quantentheorie Quantum field theory Quantum theory Statistical physics Quantenmechanik (DE-588)4047989-4 gnd rswk-swf Funktionalintegration (DE-588)4155674-4 gnd rswk-swf Quantenfeldtheorie (DE-588)4047984-5 gnd rswk-swf Quantenphysik (DE-588)4266670-3 gnd rswk-swf Quantentheorie (DE-588)4047992-4 gnd rswk-swf Statistische Physik (DE-588)4057000-9 gnd rswk-swf Funktionalintegration (DE-588)4155674-4 s DE-604 Quantenphysik (DE-588)4266670-3 s Quantentheorie (DE-588)4047992-4 s Quantenfeldtheorie (DE-588)4047984-5 s Quantenmechanik (DE-588)4047989-4 s Statistische Physik (DE-588)4057000-9 s 1\p DE-604 Jaffe, Arthur 1937- Verfasser (DE-588)1089192258 aut Erscheint auch als Online-Ausgabe 978-1-4612-4728-9 HEBIS Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001504608&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 |
| spellingShingle | Glimm, James 1934- Jaffe, Arthur 1937- Quantum physics a functional integral point of view Champs, Théorie quantique des Champs, Théorie quantique des ram Kwantummechanica gtt Kwantumveldentheorie gtt Physique statistique Physique statistique ram Quanta, Théorie des ram Statistische mechanica gtt Théorie quantique Quantentheorie Quantum field theory Quantum theory Statistical physics Quantenmechanik (DE-588)4047989-4 gnd Funktionalintegration (DE-588)4155674-4 gnd Quantenfeldtheorie (DE-588)4047984-5 gnd Quantenphysik (DE-588)4266670-3 gnd Quantentheorie (DE-588)4047992-4 gnd Statistische Physik (DE-588)4057000-9 gnd |
| subject_GND | (DE-588)4047989-4 (DE-588)4155674-4 (DE-588)4047984-5 (DE-588)4266670-3 (DE-588)4047992-4 (DE-588)4057000-9 |
| title | Quantum physics a functional integral point of view |
| title_auth | Quantum physics a functional integral point of view |
| title_exact_search | Quantum physics a functional integral point of view |
| title_full | Quantum physics a functional integral point of view James Glimm ; Arthur Jaffe |
| title_fullStr | Quantum physics a functional integral point of view James Glimm ; Arthur Jaffe |
| title_full_unstemmed | Quantum physics a functional integral point of view James Glimm ; Arthur Jaffe |
| title_short | Quantum physics |
| title_sort | quantum physics a functional integral point of view |
| title_sub | a functional integral point of view |
| topic | Champs, Théorie quantique des Champs, Théorie quantique des ram Kwantummechanica gtt Kwantumveldentheorie gtt Physique statistique Physique statistique ram Quanta, Théorie des ram Statistische mechanica gtt Théorie quantique Quantentheorie Quantum field theory Quantum theory Statistical physics Quantenmechanik (DE-588)4047989-4 gnd Funktionalintegration (DE-588)4155674-4 gnd Quantenfeldtheorie (DE-588)4047984-5 gnd Quantenphysik (DE-588)4266670-3 gnd Quantentheorie (DE-588)4047992-4 gnd Statistische Physik (DE-588)4057000-9 gnd |
| topic_facet | Champs, Théorie quantique des Kwantummechanica Kwantumveldentheorie Physique statistique Quanta, Théorie des Statistische mechanica Théorie quantique Quantentheorie Quantum field theory Quantum theory Statistical physics Quantenmechanik Funktionalintegration Quantenfeldtheorie Quantenphysik Statistische Physik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001504608&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT glimmjames quantumphysicsafunctionalintegralpointofview AT jaffearthur quantumphysicsafunctionalintegralpointofview |