Batalin-Vilkovisky formalism in locally covariant field theory:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Abschlussarbeit Buch |
| Sprache: | English |
| Veröffentlicht: |
Hamburg [u.a.]
DESY
2011
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| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | 128 S. graph. Darst. |
Internformat
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| 245 | 1 | 0 | |a Batalin-Vilkovisky formalism in locally covariant field theory |c vorgelegt von Katarzyna Anna Rejzner |
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Datensatz im Suchindex
| _version_ | 1804149078788931584 |
|---|---|
| adam_text | IMAGE 1
1 INTRODUCTION 5
P A R T I - C L A S S I C A L FIELD T H E O R Y 9
2 MATHEMATICAL PRELIMINARIES 11
2.1 FUNCTIONAL ANALYSIS 12
2.1.1 LOCALLY CONVEX VECTOR SPACES 12
2.1.2 NUCLEAR LOCALLY CONVEX VECTOR SPACES 15
2.1.3 TENSOR PRODUCTS 17
2.2 DISTRIBUTIONS 18
2.2.1 DISTRIBUTIONS ON 0 C M 18
2.2.2 VECTOR-VALUED DISTRIBUTIONS ON MANIFOLDS 20
2.2.3 DISTRIBUTIONS WITH VALUES IN A. GRADED ALGEBRA 21
2.3 INFINITE DIMENSIONAL CALCULUS 22
2.3.1 CALCULUS ON LOCALLY CONVEX VECTOR SPACES 24
2.3.2 INFINITE DIMENSIONAL LIE GROUPS 26
2.4 CATEGORIES AND FUNCTORS 27
3 CLASSICAL FIELD THEORY IN T H E LOCALLY COVARIANT FRAMEWORK 2 9
3.1 KINEMATICAL STRUCTURE 29
3.2 DYNAMICS 31
3.3 AXIOMS OF LOCALLY COVARIANT FIELD THEORY 32
3.4 POISSON STRUCTURE FOR THE FREE SCALAR FIELD 34
3.5 INTERLUDE: VECTOR VALUED FUNCTIONS ON (M) 36
3.6 FREE FERMIONIC FIELDS 36
3.7 INTERACTION 39
4 BATALIN-VILKOVISKY FORMALISM 4 3
4.1 HISTORICAL REMARKS 43
4.2 KOSZUL COMPLEX 46
4.2.1 VECTOR FIELDS ON A CONFIGURATION SPACE 46
4.2.2 IDEAL GENERATED BY THE EQUATIONS OF MOTION 48
4.2.3 ANT-IFIELDS AND ANTIBRACKET 50
4.3 SYMMETRIES 51
4.3.1 GENERAL THEORIES WITH SYMMETRIES 54
4.3.2 KOSZUL-TATE RESOLUTION 57
HTTP://D-NB.INFO/1021248878
IMAGE 2
2 CONTENTS
4.3.3 CHEVALLEY-EILENBERG COHOMOLOGY 58
4.3.4 GOING OFF-SHELL 59
4.3.5 OPEN AND CLOSED ALGEBRAS 60
4.3.6 APPENDIX: INTERPRETATION IN TERMS OF CATEGORY THEORY 61
4.4 YANG-MILLS THEORIES 63
4.4.1 GEOMETRICAL PRELIMINARIES 64
4.4.2 CHEVALLEY-EILENBERG COMPLEX 68
4.4.3 BATALIN-VILKOVISKY COMPLEX 69
4.4.4 CLASSICAL MASTER EQUATION 71
4. 4.5 GAUGE FIXING 72
4.4.6 PEIERLS BRACKET 76
4.5 CLASSICAL GRAVITY 80
4.5.1 GEOMETRICAL PRELIMINARIES 80
4.5.2 OBSERVABLES AND DIFFEOMORPHISM INVARIANCE 81
4.5.3 BV COMPLEX ON THE LEVEL OF NATURAL TRANSFORMATIONS 84
4.5.4 PEIERLS BRACKET 85
4.5.5 APPENDIX: CALCULATION OF THE EQUATIONS OF MOTION 88
P A R T I I - Q U A N T U M FIELD T H E O R Y 9 1
5 B A T A L I N - V I L K O V I S K Y F O R M A L I S M I N P A Q F T 9
3
5.1 GENERAL STRUCTURE 94
5.1.1 ALGEBRAIC FORMULATION OF PERTURBATIVE QFT 94
5.1.2 BV QUANTIZATION IN THE ALGEBRAIC FRAMEWORK 97
5.1.3 QUANTUM MASTER EQUATION AND THE QUANTUM BV OPERATOR 101 5.2
RENORMALIZATION 105
5.2.1 ALGEBRA OF OBSERVABLES 105
5.2.2 RENORMALIZED TIME ORDERED PRODUCT 107
5.2.3 ASSOCIATIVITY OF THE RENORMALIZED TIME-ORDERED PRODUCT 110 5.3 THE
RENORMALIZED QUANTUM BV OPERATOR AND THE QUANTUM MASTER EQUATION 114
5.3.1 QUANTUM FIELD THEORY ON GLOBALLY HYPERBOLIC SPACETIMES 118 5.3.2
ALGEBRAIC ADIABATIC LIMIT 119
5.3.3 QUANTUM MASTER EQUATION IN THE ALGEBRAIC ADIABATIC LIMIT 121 5.3.4
RELATION TO THE REGULARIZED Q M E 123
5.3.5 YANG-MILLS THEORY 124
C O N C L U S I O N S 1 2 7
A C K N O W L E D G E M E N T S 1 2 9
|
| any_adam_object | 1 |
| author | Rejzner, Katarzyna Anna 1985- |
| author_GND | (DE-588)1021364657 |
| author_facet | Rejzner, Katarzyna Anna 1985- |
| author_role | aut |
| author_sort | Rejzner, Katarzyna Anna 1985- |
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| building | Verbundindex |
| bvnumber | BV040119782 |
| ctrlnum | (OCoLC)794526295 (DE-599)GBV690061544 |
| dewey-full | 530.143 |
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| dewey-ones | 530 - Physics |
| dewey-raw | 530.143 |
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| dewey-sort | 3530.143 |
| dewey-tens | 530 - Physics |
| discipline | Physik |
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| spelling | Rejzner, Katarzyna Anna 1985- Verfasser (DE-588)1021364657 aut Batalin-Vilkovisky formalism in locally covariant field theory vorgelegt von Katarzyna Anna Rejzner Hamburg [u.a.] DESY 2011 128 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Hamburg, Univ., Diss., 2011 Zsfassungen in dt. und engl. Sprache (DE-588)4113937-9 Hochschulschrift gnd-content DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024975906&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Rejzner, Katarzyna Anna 1985- Batalin-Vilkovisky formalism in locally covariant field theory |
| subject_GND | (DE-588)4113937-9 |
| title | Batalin-Vilkovisky formalism in locally covariant field theory |
| title_auth | Batalin-Vilkovisky formalism in locally covariant field theory |
| title_exact_search | Batalin-Vilkovisky formalism in locally covariant field theory |
| title_full | Batalin-Vilkovisky formalism in locally covariant field theory vorgelegt von Katarzyna Anna Rejzner |
| title_fullStr | Batalin-Vilkovisky formalism in locally covariant field theory vorgelegt von Katarzyna Anna Rejzner |
| title_full_unstemmed | Batalin-Vilkovisky formalism in locally covariant field theory vorgelegt von Katarzyna Anna Rejzner |
| title_short | Batalin-Vilkovisky formalism in locally covariant field theory |
| title_sort | batalin vilkovisky formalism in locally covariant field theory |
| topic_facet | Hochschulschrift |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024975906&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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