OPE algebras:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Abschlussarbeit Buch |
| Sprache: | English |
| Veröffentlicht: |
Bonn
[Math.-Naturwiss. Fak. der Univ.]
2002
|
| Schriftenreihe: | Bonner mathematische Schriften
352 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | X, 143 S. |
Internformat
MARC
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| 245 | 1 | 0 | |a OPE algebras |c vorgelegt von Markus Rosellen |
| 246 | 1 | 3 | |a OPE-algebras |
| 264 | 1 | |a Bonn |b [Math.-Naturwiss. Fak. der Univ.] |c 2002 | |
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Datensatz im Suchindex
| _version_ | 1804129691817213952 |
|---|---|
| adam_text | Titel: OPE algebras
Autor: Rosellen, Markus
Jahr: 2002
Table of Contents
1 Introduction............................................................................................1
1.1 Overview............................................................................................1
1.2 Quantum Fields................................................................................2
1.3 OPE-Algebras..................................................................................3
1.4 The Operator Algebra of Quantum Fields..................................4
1.5 The Operator Algebra of an OPE-Algebra..................................5
1.6 Duality and Locality for Vertex Algebras....................................7
1.7 Locality for OPE-Algebras..............................................................8
1.8 Duality for OPE-Algebras..............................................................9
1.9 Examples of OPE-Algebras............................................................10
1.10 Motivation ........................................................................................11
2 The Algebra of Fields..........................................................................13
2.1 The N-Fold Module of Holomorphic Distributions......................13
2.1.1 Distributions ........................................................................13
2.1.2 S-Fold Modules....................................................................15
2.1.3 The N-Fold Module of Holomorphic Distributions .... 15
2.1.4 Commutator Formula..........................................................17
2.1.5 Operator Product Expansion ............................................17
2.1.6 State-Field Correspondence................................................18
2.1.7 Holomorphic Jacobi Identity for Distributions................19
2.1.8 Special Cases of the Holomorphic Jacobi Identity I ... 21
2.1.9 Special Cases of the Holomorphic Jacobi Identity II... 21
2.1.10 Holomorphic Duality and Holomorphic Locality............22
2.2 Conformal Symmetry......................................................................24
2.2.1 Translation Operator..........................................................24
2.2.2 Translation Covariance........................................................25
2.2.3 Derivatives............................................................................26
2.2.4 Dilatation Operator............................................................28
2.2.5 Dilatation Covariance..........................................................29
2.2.6 Gradation for Dilatation Covariant Distributions..........30
2.2.7 The Witt Algebra................................................................31
2.2.8 The Virasoro Algebra.......................................32
2.2.9 Conformal Distribution ......................................................33
2.3 Holomorphic Locality......................................................................34
VIII Table of Contents
2.3.1 The Delta Distribution............................
2.3.2 Taylor s Formula.................................
2.3.3 Locality for a Holornorphic Distribution.............
2.3.4 Holornorphic Locality.............................
2.3.5 Holornorphic Locality and OPE....................
2.3.6 Holornorphic Skew-Symmetry......................
2.3.7 Dong s Lemrna for Holornorphic Locality............
2.3.8 The Virasoro OPE ...............................
2.4 The Z-Fold Module of Holornorphic Fields.................
2.4.1 The Z-Fold Module of Holornorphic Fields...........
2.4.2 Normal Ordered Product..........................
2.4.3 Holornorphic Locality of Holomorphically Local Fields
2.4.4 Identity.........................................
2.4.5 Field-State Correspondence and Creativity..........
2.4.6 Identity Field....................................
2.5 The Partial K2-Fold Algebra of Fields.....................
2.5.1 Non-Canonical Expansions of Non-Integral Powers —
2.5.2 Canonical Expansions of Xon-Integral Powers........
2.5.3 OPE-Finite Distributions..........................
2.5.4 Reduced OPE ...................................
2.5.5 OPE of a Holornorphic Distribution.................
2.5.6 The Partial K^-Fold Algebra of Fields...............
2.5.7 The Partial IK^-Fold Algebra of Holornorphic Fields ...
2.5.8 Derivatives and Identity Field......................
2.5.9 Gradation for Dilatation Covariant Fields ...........
2.6 Locality...............................................
2.6.1 Locality.........................................
2.6.2 Creativity.......................................
2.6.3 Skew-Symmetry for Local Fields ...................
2.6.4 Goddard s Uniqueness Theorem....................
2.6.5 Dong s Lemma for Multiple Localitv................
2.6.6 Tensor Product of Fields..........................
2.6.7 Additive Locality.................................
2.6.8 Dong s Lemma for Additive Locality................
3 OPE-Algebras........................
3.1 Duality..........................
3.1.1 Skew-Symmetry for Local States.............
3.1.2 Holornorphic Jacobi Identity in terms of Distributions.
3.1.3 Duality and Additive Duality
3.1.4 Duality and Skew-Symmetry......
3.2 OPE-Algebras........................
3.2.1 OPE-Algebras..................
3.2.2 Vertex Algebras and Chiral Algebras
3.2.3 Space of Fields...................
31
36
37
33
39
40
41
42
43
43
45
46
46
43
49
50
50
51
52
54
55
56
57
5S
59
60
60
62
63
64
65
66
68
69
71
71
71
72
73
74
76
76
78
79
Table of Contents IX
3.2.4 Existence Theorem..............................................................80
3.2.5 Crossing Algebras................................................................81
3.2.6 OPE-Algebras of CFT-Type..............................................81
3.3 Additive OPE-Algebras..........................................................82
3.3.1 Additive OPE-Algebras......................................................83
3.3.2 Additive Duality and Skew-Symmetry..............................84
3.3.3 Jacobi Identity in terms of Modes....................................85
3.3.4 Jacobi Identity in terms of Distributions ........................87
3.3.5 Additive Duality and Additive Locality ..........................89
3.4 Vertex Algebras................................................................................91
3.4.1 Vertex Algebras....................................................................91
3.4.2 Modules and Vertex Algebras of Fields............................92
3.4.3 Modules over Conformal Vertex Algebras........................93
3.4.4 Commutative Vertex Algebras..........................................94
4 Structure of Vertex Algebras..........................................................97
4.1 Conformal Algebras and Local Lie Algebras................................97
4.1.1 Conformal Algebras............................................................97
4.1.2 Local Mode Algebras..........................................................98
4.1.3 Local Lie Algebras ..............................................................99
4.1.4 Superaffinization of Lie Algebras...................100
4.1.5 Affinization of Conformal Algebras.................102
4.1.6 The Mode Algebra of an N-Fold Algebra............104
4.1.7 The Local Mode Algebra of an N-Fold Algebra.......105
4.1.8 The Local Lie Algebra of a Conformal Algebra.......106
4.1.9 Free Conformal Algebras..........................107
4.1.10 Vertex Modules and Lie Algebra Modules ...........108
4.2 Conformal Algebras and Vertex Algebras..................109
4.2.1 Verma Modules and Vertex Algebras................110
4.2.2 Universal Vertex Algebra over a Local Lie Algebra.... Ill
4.2.3 Enveloping Vertex Algebras........................112
4.2.4 Free Vertex Algebras..............................113
4.2.5 Vertex Algebras defined by Linear OPEs ............114
4.2.6 Conformal Algebras defined by Linear OPEs.........116
4.2.7 Free Modules over Vertex Algebras.................117
A Superalgebra.............................................119
B Distributions and Fields..................................121
B.l Distributions and Fields.................................121
B.l.l Distributions, Test Functions, and Fields............121
B.l.2 Kernels and the Delta Distribution.................122
B.1.3 Modes of a Distribution...........................123
B.2 Distributions and Fields on Vertex Polynomials............124
B.2.1 Distributions on Vertex and Laurent Polynomials.....124
X Table of Contents
B.2.2 Vertex Series and Fields...........................125
B.2.3 Power Series Expansions of Rational Functions.......126
C Bibliographical Notes.....................................129
C.l Chapter 1.............................................129
C.2 Chapter 2.............................................130
C.3 Chapter 3.............................................132
C.4 Chapter 4.............................................133
References....................................................137
Index........................................................141
|
| any_adam_object | 1 |
| author | Rosellen, Markus |
| author_facet | Rosellen, Markus |
| author_role | aut |
| author_sort | Rosellen, Markus |
| author_variant | m r mr |
| building | Verbundindex |
| bvnumber | BV015312017 |
| classification_rvk | SI 180 |
| classification_tum | MAT 472d MAT 537d |
| ctrlnum | (OCoLC)634630950 (DE-599)BVBBV015312017 |
| discipline | Mathematik |
| format | Thesis Book |
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| indexdate | 2024-07-09T19:09:10Z |
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| language | English |
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| spelling | Rosellen, Markus Verfasser aut OPE algebras vorgelegt von Markus Rosellen OPE-algebras Bonn [Math.-Naturwiss. Fak. der Univ.] 2002 X, 143 S. txt rdacontent n rdamedia nc rdacarrier Bonner mathematische Schriften 352 Zugl.: Bonn, Univ., Diss., 2002 Vertexoperator (DE-588)4188067-5 gnd rswk-swf Konforme Differentialgeometrie (DE-588)4206468-5 gnd rswk-swf Vertexalgebra (DE-588)4328736-0 gnd rswk-swf Dimension 2 (DE-588)4321721-7 gnd rswk-swf Konforme Feldtheorie (DE-588)4312574-8 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Vertexoperator (DE-588)4188067-5 s Vertexalgebra (DE-588)4328736-0 s Konforme Differentialgeometrie (DE-588)4206468-5 s Konforme Feldtheorie (DE-588)4312574-8 s Dimension 2 (DE-588)4321721-7 s DE-604 Bonner mathematische Schriften 352 (DE-604)BV000001610 352 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010100986&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Rosellen, Markus OPE algebras Bonner mathematische Schriften Vertexoperator (DE-588)4188067-5 gnd Konforme Differentialgeometrie (DE-588)4206468-5 gnd Vertexalgebra (DE-588)4328736-0 gnd Dimension 2 (DE-588)4321721-7 gnd Konforme Feldtheorie (DE-588)4312574-8 gnd |
| subject_GND | (DE-588)4188067-5 (DE-588)4206468-5 (DE-588)4328736-0 (DE-588)4321721-7 (DE-588)4312574-8 (DE-588)4113937-9 |
| title | OPE algebras |
| title_alt | OPE-algebras |
| title_auth | OPE algebras |
| title_exact_search | OPE algebras |
| title_full | OPE algebras vorgelegt von Markus Rosellen |
| title_fullStr | OPE algebras vorgelegt von Markus Rosellen |
| title_full_unstemmed | OPE algebras vorgelegt von Markus Rosellen |
| title_short | OPE algebras |
| title_sort | ope algebras |
| topic | Vertexoperator (DE-588)4188067-5 gnd Konforme Differentialgeometrie (DE-588)4206468-5 gnd Vertexalgebra (DE-588)4328736-0 gnd Dimension 2 (DE-588)4321721-7 gnd Konforme Feldtheorie (DE-588)4312574-8 gnd |
| topic_facet | Vertexoperator Konforme Differentialgeometrie Vertexalgebra Dimension 2 Konforme Feldtheorie Hochschulschrift |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010100986&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000001610 |
| work_keys_str_mv | AT rosellenmarkus opealgebras |