Quantum fields on a lattice:
This book presents a comprehensive and coherent account of the theory of quantum fields on a lattice, an essential technique for the study of the strong and electroweak nuclear interactions
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cambridge
Cambridge Univ. Press
1994
|
| Ausgabe: | 1. publ. |
| Schriftenreihe: | Cambridge monographs on mathematical physics
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Zusammenfassung: | This book presents a comprehensive and coherent account of the theory of quantum fields on a lattice, an essential technique for the study of the strong and electroweak nuclear interactions Quantum field theory describes basic physical phenomena over an extremely wide range of length or energy scales. Quantum fields exist in space and time, which can be approximated by a set of lattice points. This approximation allows the application of powerful analytical and numerical techniques, and has provided a powerful tool for the study of both the strong and the electroweak interaction After introductory chapters on scalar fields, gauge fields and fermion fields, the book studies quarks and gluons in QCD and fermions and bosons in the electroweak theory. The last chapter is devoted to numerical simulation algorithms which have been used in recent large-scale numerical simulations |
| Beschreibung: | XIII, 491 S. graph. Darst. |
| ISBN: | 0521404320 |
Internformat
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| 245 | 1 | 0 | |a Quantum fields on a lattice |c István Montvay ; Gernot Münster |
| 250 | |a 1. publ. | ||
| 264 | 1 | |a Cambridge |b Cambridge Univ. Press |c 1994 | |
| 300 | |a XIII, 491 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Cambridge monographs on mathematical physics | |
| 520 | 3 | |a This book presents a comprehensive and coherent account of the theory of quantum fields on a lattice, an essential technique for the study of the strong and electroweak nuclear interactions | |
| 520 | |a Quantum field theory describes basic physical phenomena over an extremely wide range of length or energy scales. Quantum fields exist in space and time, which can be approximated by a set of lattice points. This approximation allows the application of powerful analytical and numerical techniques, and has provided a powerful tool for the study of both the strong and the electroweak interaction | ||
| 520 | |a After introductory chapters on scalar fields, gauge fields and fermion fields, the book studies quarks and gluons in QCD and fermions and bosons in the electroweak theory. The last chapter is devoted to numerical simulation algorithms which have been used in recent large-scale numerical simulations | ||
| 650 | 7 | |a Champ cristallin, Théorie du |2 ram | |
| 650 | 4 | |a Champs de jauge (Physique) | |
| 650 | 7 | |a Champs de jauge (physique) |2 ram | |
| 650 | 4 | |a Champs sur réseau, Théorie des | |
| 650 | 4 | |a Champs, Théorie quantique des | |
| 650 | 7 | |a Champs, Théorie quantique des |2 ram | |
| 650 | 4 | |a Chromodynamique quantique | |
| 650 | 7 | |a Interactions faibles |2 ram | |
| 650 | 4 | |a Interactions électrofaibles | |
| 650 | 7 | |a Interactions électrofaibles |2 ram | |
| 650 | 7 | |a Kwantumveldentheorie |2 gtt | |
| 650 | 4 | |a Modèles collectifs (Physique nucléaire) | |
| 650 | 7 | |a Roostermodellen |2 gtt | |
| 650 | 7 | |a Treillis, Théorie des |2 ram | |
| 650 | 4 | |a Electroweak interactions | |
| 650 | 4 | |a Gauge fields (Physics) | |
| 650 | 4 | |a Lattice field theory | |
| 650 | 4 | |a Quantum field theory | |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-006430874 | ||
Datensatz im Suchindex
| _version_ | 1804124070227214336 |
|---|---|
| adam_text | CONTENTS PREFACE XIII 1 INTRODUCTION 1 1.1 HISTORICAL REMARKS 1 1.2 PATH
INTEGRAL IN QUANTUM MECHANICS 3 1.2.1 FEYNMAN PATH INTEGRAL 3 1.2.2
EUCLIDEAN PATH INTEGRAL 6 1.3 EUCLIDEAN QUANTUM FIELD THEORY 8 1.3.1
SCALAR FIELDS 9 1.3.2 SCHWINGER FUNCTIONS 10 1.3.3 WICK ROTATION 12
1.3.4 FREE FIELD 14 1.3.5 REFLECTION POSITIVITY 14 1.4 EUCLIDEAN
FUNCTIONAL INTEGRALS 16 1.4.1 GAUSSIAN INTEGRALS 16 1.4.2 EUCLIDEAN FREE
FIELD 18 1.4.3 FUNCTIONAL INTEGRAL FOR THE EUCLIDEAN FREE FIELD 21 1.4.4
FUNCTIONAL INTEGRAL FOR THE INTERACTING FIELD 22 1.4.5 PERTURBATION
THEORY 24 1.5 QUANTUM FIELD THEORY ON A LATTICE 26 1.5.1 LATTICE
REGULARIZATION 26 1.5.2 TRANSFER MATRIX 29 1.5.3 REFLECTION POSITIVITY
31 1.6 CONTINUUM LIMIT AND CRITICAL BEHAVIOUR 34 1.6.1 LATTICE FIELD
THEORY AND STATISTICAL SYSTEMS 34 1.6.2 RENORMALIZATION AND CRITICAL
BEHAVIOUR 36 1.6.3 UNIVERSALITY 39 1.7 RENORMALIZATION GROUP EQUATIONS
41 1.7.1 RENORMALIZATION GROUP EQUATIONS FOR THE BARE THEORY 41 1.7.2
CALLAN-SYMANZIK EQUATIONS 43 1.7.3 RENORMALIZATION GROUP EQUATIONS FOR A
MASSLESS THEORY 45 1.7.4 FIXED POINTS 46 1.8 THERMODYNAMICS OF QUANTUM
FIELDS 49 1.8.1 FIELD THEORY AT FINITE PHYSICAL TEMPERATURE 49 1.8.2
ANISOTROPIC LATTICE REGULARIZATION 51 2 SCALAR FIELDS 54 2.1 PHI 4 MODEL
ON THE LATTICE 54 2.1.1 GREEN S FUNCTIONS 55 2.1.2 PARTICLE STATES 58
2.1.3 RENORMALIZED QUANTITIES 60 2.2 PERTURBATION THEORY 62 2.2.1 FREE
FIELD THEORY 62 2.2.2 PERTURBATION THEORY IN THE SYMMETRIC PHASE 64
2.2.3 PERTURBATION THEORY IN THE PHASE WITH BROKEN SYMMETRY 70 2.3
HOPPING PARAMETER EXPANSIONS 74 2.4 LIISCHER-WEISZ SOLUTION AND
TRIVIALITY OF THE CONTINUUM LIMIT 77 2.4.1 TRIVIALITY OF
FOUR-DIMENSIONAL PHI 4 THEORY 77 2.4.2 INFINITE BARE COUPLING LIMIT 80
2.5 FINITE-VOLUME EFFECTS 81 2.5.1 PERTURBATIVE FINITE-VOLUME EFFECTS 82
2.5.2 TUNNELING 85 2.6 TV-COMPONENT MODEL 87 3 GAUGE FIELDS 91 3.1
CONTINUUM GAUGE FIELDS 91 3.1.1 SU(N) GAUGE FIELDS 91 3.1.2 ABELIAN
GAUGE FIELDS 96 3.2 LATTICE GAUGE FIELDS AND WILSON S ACTION 97 3.2.1
LATTICE GAUGE FIELDS 97 3.2.2 WILSON S ACTION 99 3.2.3 FUNCTIONAL
INTEGRAL 101 3.2.4 OBSERVABLES 105 3.2.5 GAUGE FIXING 1.07 3.2.6
TRANSFER MATRIX 108 3.2.7 GROUP CHARACTERS 110 3.2.8 REFLECTION
POSITIVITY 113 3.2.9 OTHER ACTIONS 114 3.3 PERTURBATION THEORY 116 3.3.1
FEYNMAN RULES 117 3.3.2 RENORMALIZATION GROUP 124 3.3.3
LAMBDA-PARAMETERS 128 3.4 STRONG-COUPLING EXPANSION 130 3.4.1
HIGH-TEMPERATURE EXPANSIONS 130 3.4.2 STRONG-COUPLING GRAPHS 131 3.4.3
MOMENTS AND CUMULANTS 135 3.4.4 CLUSTER EXPANSION FOR THE FREE ENERGY
138 3A5 RESULTS FROM THE STRONG-COUPLING EXPANSION 141 3.5 STATIC QUARK
POTENTIAL 142 3.5.1 WILSON LOOP CRITERION 142 3.5.2 STRONG-COUPLING
EXPANSION 146 3.5.3 ROUGHENING TRANSITION 150 3.5.4 NUMERICAL
INVESTIGATIONS 152 3.6 GLUEBALL SPECTRUM 153 3.6.1 GLUEBALL STATES 153
3.6.2 STRONG-COUPLING EXPANSION 156 3.6.3 MONTE CARLO RESULTS 159 3.7
PHASE STRUCTURE OF LATTICE GAUGE THEORY 160 3.7.1 GENERAL RESULTS 161
3.7.2 ABELIAN GAUGE GROUPS 162 3.7.3 NON-ABELIAN GAUGE GROUPS 163 4
FERMION FIELDS 164 4.1 FERMIONIC VARIABLES 164 4.1.1 CREATION AND
ANNIHILATION OPERATORS 164 4.1.2 A SIMPLE EXAMPLE 165 4.1.3 GRASSMANN
VARIABLES 166 4.1.4 POLYMER REPRESENTATION 171 42 WILSON FERMIONS 174
4.2.1 HAMILTONIAN FORMULATION 175 4.2.2 EUCLIDEAN FORMULATION: WILSON
ACTION 178 4.2.3 REFLECTION POSITIVITY OF THE WILSON ACTION 182 42.4
WILSON FERMION PROPAGATOR AND GREEN FUNCTIONS 187 42.5 TIMESLICES OF
WILSON FERMIONS 192 43 KOGUT-SUSSKIND STAGGERED FERMIONS 195 4.3.1 FROM
NAIVE TO STAGGERED FERMIONS 196 43.2 FLAVOURS OF STAGGERED FERMIONS 199
4.3.3 CONNECTION TO THE DIRAC-KAEHLER EQUATION 205 44 NIELSEN-NINOMIYA
THEOREM AND MIRROR FERMIONS 208 4.4.1 DOUBLERS IN LATTICE FERMION
PROPAGATORS 208 442 DOUBLERS AND. THE AXIAL ANOMALY 213 4.5 QED ON THE
LATTICE 218 4.5.1 LATTICE ACTIONS 221 45.2 ANALYTIC RESULTS 225 45.3
NON-PERTURBATIVE STUDIES 228 5 QUANTUM CHROMODYNAMICS 231 5.1 LATTICE
ACTION AND CONTINUUM LIMIT 232 5.1.1 LATTICE ACTIONS 232 5.1.2 QUENCHED
APPROXIMATION 235 5.1.3 HOPPING PARAMETER EXPANSION 238 5.1.4 STRONG
GAUGE COUPLING LIMIT 241 5.1.5 LATTICE PERTURBATION THEORY 244 5.1.6
CONTINUUM LIMIT 249 5.2 HADRON SPECTRUM 257 5.2.1 HADRONIC TWO-POINT
FUNCTIONS 258 5.2.2 HADRON SOURCES 266 5.2.3 HEAVY QUARK SYSTEMS 270 5.3
BROKEN CHIRAL SYMMETRY ON THE LATTICE 273 5.3.1 WARD-TAKAHASHI
IDENTITIES 275 5.3.2 PCAC AND THE QUARK MASS 282 5.3.3 CURRENT ALGEBRA
286 5.3.4 SCALAR DENSITIES 290 5.3.5 THE U(L) PROBLEM 292 5.3.6 CURRENT
MATRIX ELEMENTS 294 5.4 HADRON THERMODYNAMICS 297 5.4.1 HADRON
THERMODYNAMICS ON THE LATTICE 299 5.4.2 DECONFINEMENT AND CHIRAL
SYMMETRY RESTORATION 307 5.4.3 NON-ZERO QUARK NUMBER DENSITY 312 6 HIGGS
AND YUKAWA MODELS 318 6.1 LATTICE HIGGS MODELS 319 6.1.1 LATTICE ACTIONS
320 6.1.2 LATTICE PERTURBATION THEORY 326 6.1.3 PHASE STRUCTURE AND
SYMMETRY RESTORATION 333 6.1.4 TRIVIALITY UPPER BOUND 339 6.1.5 WEAK
GAUGE COUPLING LIMIT 344 6.2 LATTICE YUKAWA MODELS 350 6.2.1 LATTICE
ACTIONS 351 6.2.2 THE GOLTERMAN-PETCHER THEOREM 358 6.2.3 NUMERICAL
SIMULATIONS, PHASE STRUCTURE 363 6.2.4 VACUUM STABILITY LOWER BOUND 369
7 SIMULATION ALGORITHMS 374 7.1 NUMERICAL SIMULATION AND MARKOV
PROCESSES 374 7.1.1 UPDATING PROCESSES 376 7.1.2 UPDATING WITH
CONSTRAINTS 380 7.1.3 ERROR ESTIMATES 381 7.1.4 IMPROVED ESTIMATORS 389
7.2 METROPOLIS ALGORITHMS 391 7.3 HEATBATH ALGORITHMS 396 7.3.1 HEATBATH
IN LATTICE GAUGE THEORIES 399 7.4 FERMIONS IN NUMERICAL SIMULATIONS 403
7.4.1 FERMION MATRIX INVERSION 408 7.5 FERMION ALGORITHMS BASED ON
DIFFERENTIAL EQUATIONS 413 7.5.1 CLASSICAL DYNAMICS ALGORITHMS 413 7.5.2
LANGEVIN ALGORITHMS 416 7.6 HYBRID MONTE CARLO ALGORITHMS 421 7.6.1 HMC
FOR SCALAR FIELDS 422 7.6.2 HMC FOR GAUGE AND FERMION FIELDS 426 7.7
CLUSTER ALGORITHMS 427 8 APPENDIX 434 8.1 NOTATION CONVENTIONS AND BASIC
FORMULAS 434 8.1.1 PAULI MATRICES 434 8.1.2 DIRAC MATRICES 434 8.1.3 LIE
ALGEBRA GENERATORS 435 8.1.4 CONTINUUM, GAUGE FIELDS 436 8.1.5 LATTICE
NOTATIONS 437 8.1.6 FREE FIELDS 439 8.1.7 REDUCTION FORMULAS 441
REFERENCES 443 INDEX 486
|
| any_adam_object | 1 |
| author | Montvay, I. 1940- Münster, Gernot 1952- |
| author_GND | (DE-588)112885594 (DE-588)110621638 |
| author_facet | Montvay, I. 1940- Münster, Gernot 1952- |
| author_role | aut aut |
| author_sort | Montvay, I. 1940- |
| author_variant | i m im g m gm |
| building | Verbundindex |
| bvnumber | BV009723234 |
| callnumber-first | Q - Science |
| callnumber-label | QC793 |
| callnumber-raw | QC793.3.F5 |
| callnumber-search | QC793.3.F5 |
| callnumber-sort | QC 3793.3 F5 |
| callnumber-subject | QC - Physics |
| classification_rvk | UO 4000 UO 4020 |
| classification_tum | PHY 023f |
| ctrlnum | (OCoLC)28221996 (DE-599)BVBBV009723234 |
| dewey-full | 530.1/43 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 530 - Physics |
| dewey-raw | 530.1/43 |
| dewey-search | 530.1/43 |
| dewey-sort | 3530.1 243 |
| dewey-tens | 530 - Physics |
| discipline | Physik |
| edition | 1. publ. |
| format | Book |
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| id | DE-604.BV009723234 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T17:39:49Z |
| institution | BVB |
| isbn | 0521404320 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-006430874 |
| oclc_num | 28221996 |
| open_access_boolean | |
| owner | DE-91G DE-BY-TUM DE-384 DE-355 DE-BY-UBR DE-703 DE-20 DE-19 DE-BY-UBM DE-11 DE-188 |
| owner_facet | DE-91G DE-BY-TUM DE-384 DE-355 DE-BY-UBR DE-703 DE-20 DE-19 DE-BY-UBM DE-11 DE-188 |
| physical | XIII, 491 S. graph. Darst. |
| publishDate | 1994 |
| publishDateSearch | 1994 |
| publishDateSort | 1994 |
| publisher | Cambridge Univ. Press |
| record_format | marc |
| series2 | Cambridge monographs on mathematical physics |
| spelling | Montvay, I. 1940- Verfasser (DE-588)112885594 aut Quantum fields on a lattice István Montvay ; Gernot Münster 1. publ. Cambridge Cambridge Univ. Press 1994 XIII, 491 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Cambridge monographs on mathematical physics This book presents a comprehensive and coherent account of the theory of quantum fields on a lattice, an essential technique for the study of the strong and electroweak nuclear interactions Quantum field theory describes basic physical phenomena over an extremely wide range of length or energy scales. Quantum fields exist in space and time, which can be approximated by a set of lattice points. This approximation allows the application of powerful analytical and numerical techniques, and has provided a powerful tool for the study of both the strong and the electroweak interaction After introductory chapters on scalar fields, gauge fields and fermion fields, the book studies quarks and gluons in QCD and fermions and bosons in the electroweak theory. The last chapter is devoted to numerical simulation algorithms which have been used in recent large-scale numerical simulations Champ cristallin, Théorie du ram Champs de jauge (Physique) Champs de jauge (physique) ram Champs sur réseau, Théorie des Champs, Théorie quantique des Champs, Théorie quantique des ram Chromodynamique quantique Interactions faibles ram Interactions électrofaibles Interactions électrofaibles ram Kwantumveldentheorie gtt Modèles collectifs (Physique nucléaire) Roostermodellen gtt Treillis, Théorie des ram Electroweak interactions Gauge fields (Physics) Lattice field theory Quantum field theory Gitterfeldtheorie (DE-588)4296098-8 gnd rswk-swf Gitterfeldtheorie (DE-588)4296098-8 s DE-604 Münster, Gernot 1952- Verfasser (DE-588)110621638 aut OEBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006430874&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Montvay, I. 1940- Münster, Gernot 1952- Quantum fields on a lattice Champ cristallin, Théorie du ram Champs de jauge (Physique) Champs de jauge (physique) ram Champs sur réseau, Théorie des Champs, Théorie quantique des Champs, Théorie quantique des ram Chromodynamique quantique Interactions faibles ram Interactions électrofaibles Interactions électrofaibles ram Kwantumveldentheorie gtt Modèles collectifs (Physique nucléaire) Roostermodellen gtt Treillis, Théorie des ram Electroweak interactions Gauge fields (Physics) Lattice field theory Quantum field theory Gitterfeldtheorie (DE-588)4296098-8 gnd |
| subject_GND | (DE-588)4296098-8 |
| title | Quantum fields on a lattice |
| title_auth | Quantum fields on a lattice |
| title_exact_search | Quantum fields on a lattice |
| title_full | Quantum fields on a lattice István Montvay ; Gernot Münster |
| title_fullStr | Quantum fields on a lattice István Montvay ; Gernot Münster |
| title_full_unstemmed | Quantum fields on a lattice István Montvay ; Gernot Münster |
| title_short | Quantum fields on a lattice |
| title_sort | quantum fields on a lattice |
| topic | Champ cristallin, Théorie du ram Champs de jauge (Physique) Champs de jauge (physique) ram Champs sur réseau, Théorie des Champs, Théorie quantique des Champs, Théorie quantique des ram Chromodynamique quantique Interactions faibles ram Interactions électrofaibles Interactions électrofaibles ram Kwantumveldentheorie gtt Modèles collectifs (Physique nucléaire) Roostermodellen gtt Treillis, Théorie des ram Electroweak interactions Gauge fields (Physics) Lattice field theory Quantum field theory Gitterfeldtheorie (DE-588)4296098-8 gnd |
| topic_facet | Champ cristallin, Théorie du Champs de jauge (Physique) Champs de jauge (physique) Champs sur réseau, Théorie des Champs, Théorie quantique des Chromodynamique quantique Interactions faibles Interactions électrofaibles Kwantumveldentheorie Modèles collectifs (Physique nucléaire) Roostermodellen Treillis, Théorie des Electroweak interactions Gauge fields (Physics) Lattice field theory Quantum field theory Gitterfeldtheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006430874&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT montvayi quantumfieldsonalattice AT munstergernot quantumfieldsonalattice |