Path integrals and anomalies in curved space:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge [u.a.]
Cambridge Univ. Press
2006
|
| Edition: | 1. publ. |
| Series: | Cambridge monographs on mathematical physics
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XVII, 379 S. graph. Darst. |
| ISBN: | 0521847613 9780521847612 |
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| adam_text | PATH INTEGRALS AND ANOMALIES IN CURVED SPACE FIORENZO BASTIANELLI
UNIVERSITA DEGLI STUDI, BOLOGNA, ITALY PETER VAN NIEUWENHUIZEN STATE
UNIVERSITY OF NEW YORK AT STONY BROOK CAMBRIDGE UNIVERSITY PRESS
CONTENTS PREFACE XI PART I PATH INTEGRALS FOR QUANTUM MECHANICS IN
CURVED SPACE 1 1 INTRODUCTION TO PATH INTEGRALS 3 1.1 THE SIMPLEST CASE:
A PARTICLE IN FLAT SPACE 5 1.2 QUANTUM MECHANICAL PATH INTEGRALS IN
CURVED SPACE REQUIRE REGULARIZATION 9 1.3 POWER COUNTING AND DIVERGENCES
18 1.4 BRIEF SUMMARY OF THE THREE REGULARIZATION SCHEMES 23 1.5 A BRIEF
HISTORY OF PATH INTEGRALS 27 2 TIME SLICING 33 2.1 CONFIGURATION-SPACE
PATH INTEGRALS FOR BOSONS FROM TIME SLICING 34 2.2 THE PHASE-SPACE PATH
INTEGRAL AND MATTHEWS THEOREM 60 2.3 PATH INTEGRALS FOR DIRAC FERMIONS
73 2.4 PATH INTEGRALS FOR MAJOR ANA FERMIONS 82 2.5 DIRECT EVALUATION OF
THE TRANSITION ELEMENT TO ORDER F3 86 2.6 TWO-LOOP PATH INTEGRAL
EVALUATION OF THE TRANSITION ELEMENT TO ORDER (3 98 3 MODE
REGULARIZATION 108 3.1 MODE REGULARIZATION IN CONFIGURATION SPACE 109
3.2 THE TWO-LOOP AMPLITUDE AND THE COUNTERTERM VMR 116 3.3 CALCULATION
OF FEYNMAN GRAPHS IN MODE REGULARIZATION 123 VII VIII CONTENTS 4
DIMENSIONAL REGULARIZATION 127 4.1 DIMENSIONAL REGULARIZATION IN
CONFIGURATION SPACE 128 4.2 TWO-LOOP TRANSITION AMPLITUDE AND THE
COUNTERTERM VDR 133 4.3 CALCULATION OF FEYNMAN GRAPHS IN DIMENSIONAL
REGULARIZATION - 134 4.4 PATH INTEGRALS FOR FERMIONS 136 PART II
APPLICATIONS TO ANOMALIES 145 5 INTRODUCTION TO ANOMALIES 147 5.1 THE
SIMPLEST CASE: ANOMALIES IN TWO DIMENSIONS 149 5.2 THE FUJIKAWA METHOD
163 5.3 HOW TO CALCULATE ANOMALIES USING QUANTUM MECHANICS 167 5.4 A
BRIEF HISTORY OF ANOMALIES 177 6 CHIRAL ANOMALIES FROM SUSY QUANTUM
MECHANICS 185 6.1 THE ABELIAN CHIRAL ANOMALY FOR SPIN-^ FIELDS COUPLED
TO GRAVITY IN 4FC DIMENSIONS 185 6.2 THE ABELIAN CHIRAL ANOMALY FOR
SPIN- FIELDS COUPLED TO THE YANG-MILLS FIELDS IN 2K DIMENSIONS 200 6.3
LORENTZ ANOMALIES FOR CHIRAL SPIN-5 FIELDS COUPLED TO GRAVITY IN 4 K + 2
DIMENSIONS 211 6.4 MIXED LORENTZ AND NON-ABELIAN GAUGE ANOMALIES FOR
CHIRAL SPIN-^ FIELDS COUPLED TO GRAVITY AND YANG-MILLS FIELDS IN 2K
DIMENSIONS - 219 6.5 THE ABELIAN CHIRAL ANOMALY FOR SPIN-| FIELDS
COUPLED TO GRAVITY IN 4FC DIMENSIONS 223 6.6 LORENTZ ANOMALIES FOR
CHIRAL SPIN-| FIELDS COUPLED TO GRAVITY IN 4K + 2 DIMENSIONS 231 6.7
LORENTZ ANOMALIES FOR SELF-DUAL ANTISYMMETRIC TENSOR FIELDS COUPLED TO
GRAVITY IN 4A; + 2 DIMENSIONS 237 6.8 CANCELLATION OF GRAVITATIONAL
ANOMALIES IN IIB SUPERGRAVITY 249 6.9 CANCELLATION OF ANOMALIES IN N = 1
SUPERGRAVITY 252 6.10 THE 50(16) X 5O(16) STRING , 273 6.11 INDEX
THEOREMS AND PATH INTEGRALS 277 7 TRACE ANOMALIES FROM ORDINARY AND SUSY
QUANTUM MECHANICS 285 7.1 TRACE ANOMALIES FOR SCALAR FIELDS IN TWO AND
FOUR DIMENSIONS 286 CONTENTS IX 7.2 TRACE ANOMALIES FOR SPIN-5 FIELDS IN
TWO AND FOUR DIMENSIONS 293 7.3 TRACE ANOMALIES FOR A VECTOR FIELD IN
FOUR DIMENSIONS 298 7.4 STRING-INSPIRED APPROACH TO TRACE ANOMALIES 303
8 CONCLUSIONS AND SUMMARY 312 APPENDICES 320 A RIEMANN CURVATURES 320 B
WEYL ORDERING OF BOSONIC OPERATORS 325 C WEYL ORDERING OF FERMIONIC
OPERATORS 331 D NONLINEAR SUSY SIGMA MODELS AND D = 1 SUPERSPACE 336 E
NONLINEAR SUSY SIGMA MODELS FOR INTERNAL SYMMETRIES 348 F GAUGE
ANOMALIES FOR EXCEPTIONAL GROUPS 352 REFERENCES 366 INDEX 377
|
| adam_txt |
PATH INTEGRALS AND ANOMALIES IN CURVED SPACE FIORENZO BASTIANELLI
UNIVERSITA DEGLI STUDI, BOLOGNA, ITALY PETER VAN NIEUWENHUIZEN STATE
UNIVERSITY OF NEW YORK AT STONY BROOK CAMBRIDGE UNIVERSITY PRESS
CONTENTS PREFACE XI PART I PATH INTEGRALS FOR QUANTUM MECHANICS IN
CURVED SPACE 1 1 INTRODUCTION TO PATH INTEGRALS 3 1.1 THE SIMPLEST CASE:
A PARTICLE IN FLAT SPACE 5 1.2 QUANTUM MECHANICAL PATH INTEGRALS IN
CURVED SPACE REQUIRE REGULARIZATION 9 1.3 POWER COUNTING AND DIVERGENCES
18 1.4 BRIEF SUMMARY OF THE THREE REGULARIZATION SCHEMES 23 1.5 A BRIEF
HISTORY OF PATH INTEGRALS 27 2 TIME SLICING 33 2.1 CONFIGURATION-SPACE
PATH INTEGRALS FOR BOSONS FROM TIME SLICING 34 2.2 THE PHASE-SPACE PATH
INTEGRAL AND MATTHEWS' THEOREM 60 2.3 PATH INTEGRALS FOR DIRAC FERMIONS
73 2.4 PATH INTEGRALS FOR MAJOR ANA FERMIONS 82 2.5 DIRECT EVALUATION OF
THE TRANSITION ELEMENT TO ORDER F3 86 2.6 TWO-LOOP PATH INTEGRAL
EVALUATION OF THE TRANSITION ELEMENT TO ORDER (3 98 3 MODE
REGULARIZATION 108 3.1 MODE REGULARIZATION IN CONFIGURATION SPACE 109
3.2 THE TWO-LOOP AMPLITUDE AND THE COUNTERTERM VMR 116 3.3 CALCULATION
OF FEYNMAN GRAPHS IN MODE REGULARIZATION 123 VII VIII CONTENTS 4
DIMENSIONAL REGULARIZATION 127 4.1 DIMENSIONAL REGULARIZATION IN
CONFIGURATION SPACE 128 4.2 TWO-LOOP TRANSITION AMPLITUDE AND THE
COUNTERTERM VDR 133 4.3 CALCULATION OF FEYNMAN GRAPHS IN DIMENSIONAL
REGULARIZATION - 134 4.4 PATH INTEGRALS FOR FERMIONS 136 PART II
APPLICATIONS TO ANOMALIES 145 5 INTRODUCTION TO ANOMALIES 147 5.1 THE
SIMPLEST CASE: ANOMALIES IN TWO DIMENSIONS 149 5.2 THE FUJIKAWA METHOD
163 5.3 HOW TO CALCULATE ANOMALIES USING QUANTUM MECHANICS 167 5.4 A
BRIEF HISTORY OF ANOMALIES 177 6 CHIRAL ANOMALIES FROM SUSY QUANTUM
MECHANICS 185 6.1 THE ABELIAN CHIRAL ANOMALY FOR SPIN-^ FIELDS COUPLED
TO GRAVITY IN 4FC DIMENSIONS 185 6.2 THE ABELIAN CHIRAL ANOMALY FOR
SPIN- \ FIELDS COUPLED TO THE YANG-MILLS FIELDS IN 2K DIMENSIONS 200 6.3
LORENTZ ANOMALIES FOR CHIRAL SPIN-5 FIELDS COUPLED TO GRAVITY IN 4 K + 2
DIMENSIONS 211 6.4 MIXED LORENTZ AND NON-ABELIAN GAUGE ANOMALIES FOR
CHIRAL SPIN-^ FIELDS COUPLED TO GRAVITY AND YANG-MILLS FIELDS IN 2K
DIMENSIONS - 219 6.5 THE ABELIAN CHIRAL ANOMALY FOR SPIN-| FIELDS
COUPLED TO GRAVITY IN 4FC DIMENSIONS 223 6.6 LORENTZ ANOMALIES FOR
CHIRAL SPIN-| FIELDS COUPLED TO GRAVITY IN 4K + 2 DIMENSIONS 231 6.7
LORENTZ ANOMALIES FOR SELF-DUAL ANTISYMMETRIC TENSOR FIELDS COUPLED TO
GRAVITY IN 4A; + 2 DIMENSIONS 237 6.8 CANCELLATION OF GRAVITATIONAL
ANOMALIES IN IIB SUPERGRAVITY 249 6.9 CANCELLATION OF ANOMALIES IN N = 1
SUPERGRAVITY 252 6.10 THE 50(16) X 5O(16) STRING , 273 6.11 INDEX
THEOREMS AND PATH INTEGRALS 277 7 TRACE ANOMALIES FROM ORDINARY AND SUSY
QUANTUM MECHANICS 285 7.1 TRACE ANOMALIES FOR SCALAR FIELDS IN TWO AND
FOUR DIMENSIONS 286 CONTENTS IX 7.2 TRACE ANOMALIES FOR SPIN-5 FIELDS IN
TWO AND FOUR DIMENSIONS 293 7.3 TRACE ANOMALIES FOR A VECTOR FIELD IN
FOUR DIMENSIONS 298 7.4 STRING-INSPIRED APPROACH TO TRACE ANOMALIES 303
8 CONCLUSIONS AND SUMMARY 312 APPENDICES 320 A RIEMANN CURVATURES 320 B
WEYL ORDERING OF BOSONIC OPERATORS 325 C WEYL ORDERING OF FERMIONIC
OPERATORS 331 D NONLINEAR SUSY SIGMA MODELS AND D = 1 SUPERSPACE 336 E
NONLINEAR SUSY SIGMA MODELS FOR INTERNAL SYMMETRIES 348 F GAUGE
ANOMALIES FOR EXCEPTIONAL GROUPS 352 REFERENCES 366 INDEX 377 |
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| id | DE-604.BV020857384 |
| illustrated | Illustrated |
| index_date | 2024-07-02T13:21:47Z |
| indexdate | 2024-07-09T20:26:47Z |
| institution | BVB |
| isbn | 0521847613 9780521847612 |
| language | English |
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| spelling | Bastianelli, Fiorenzo Verfasser aut Path integrals and anomalies in curved space Fiorenzo Bastianelli ; Peter van Nieuwenhuizen 1. publ. Cambridge [u.a.] Cambridge Univ. Press 2006 XVII, 379 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Cambridge monographs on mathematical physics Courbes Intégrales de chemin Curves Path integrals Gekrümmte Raumzeit (DE-588)4322953-0 gnd rswk-swf Pfadintegral (DE-588)4173973-5 gnd rswk-swf Quantenfeldtheorie (DE-588)4047984-5 gnd rswk-swf Pfadintegral (DE-588)4173973-5 s Gekrümmte Raumzeit (DE-588)4322953-0 s Quantenfeldtheorie (DE-588)4047984-5 s DE-604 Van Nieuwenhuizen, Peter Verfasser aut GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014178997&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Bastianelli, Fiorenzo Van Nieuwenhuizen, Peter Path integrals and anomalies in curved space Courbes Intégrales de chemin Curves Path integrals Gekrümmte Raumzeit (DE-588)4322953-0 gnd Pfadintegral (DE-588)4173973-5 gnd Quantenfeldtheorie (DE-588)4047984-5 gnd |
| subject_GND | (DE-588)4322953-0 (DE-588)4173973-5 (DE-588)4047984-5 |
| title | Path integrals and anomalies in curved space |
| title_auth | Path integrals and anomalies in curved space |
| title_exact_search | Path integrals and anomalies in curved space |
| title_exact_search_txtP | Path integrals and anomalies in curved space |
| title_full | Path integrals and anomalies in curved space Fiorenzo Bastianelli ; Peter van Nieuwenhuizen |
| title_fullStr | Path integrals and anomalies in curved space Fiorenzo Bastianelli ; Peter van Nieuwenhuizen |
| title_full_unstemmed | Path integrals and anomalies in curved space Fiorenzo Bastianelli ; Peter van Nieuwenhuizen |
| title_short | Path integrals and anomalies in curved space |
| title_sort | path integrals and anomalies in curved space |
| topic | Courbes Intégrales de chemin Curves Path integrals Gekrümmte Raumzeit (DE-588)4322953-0 gnd Pfadintegral (DE-588)4173973-5 gnd Quantenfeldtheorie (DE-588)4047984-5 gnd |
| topic_facet | Courbes Intégrales de chemin Curves Path integrals Gekrümmte Raumzeit Pfadintegral Quantenfeldtheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014178997&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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