Factorization algebras in quantum field theory: Volume 1 Factorization algebras in quantum field theory
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge
Cambridge University Press
2017
|
| Series: | New mathematical monographs
31 |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | IX, 387 Seiten |
| ISBN: | 9781107163102 |
Staff View
MARC
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Record in the Search Index
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Contents 1 Introduction 1.1 The Motivating Example of Quantum Mechanics 1.2 A Preliminary Definition of Prefactorization Algebras 1.3 Prefactorization Algebras in Quantum Field Theory 1.4 Comparisons with Other Formalizations of Quantum Field Theory 1.5 Overview of This Volume 1.6 Acknowledgments PARTI PREFACTORIZATION ALGEBRAS 2 From Gaussian Measures to Factorization Algebras 2.1 Gaussian Integrals in Finite Dimensions 2.2 Divergence in Infinite Dimensions 2.3 The Prefactorization Structure on Observables 2.4 From Quantum to Classical 2.5 Correlation Functions 2.6 Further Results on Free Field Theories 2.7 Interacting Theories 3 Prefactorization Algebras and Basic Examples 3.1 Prefactorization Algebras 3.2 Associative Algebras fromPrefactorization Algebras on R 3.3 Modules as Defects 3.4 A Construction of the Universal Enveloping Algebra 3.5 Some Functional Analysis vii page 1 З 8 8 11 16 18 21 23 25 27 31 34 36 39 40 44 44 51 52 59 62
Contents viii The Factorization Envelope of a Sheaf of Lie Algebras Equivariant Prefactorization Algebras 73 79 PART II FIRST EXAMPLES OF FIELD THEORIES AND THEIR OBSERVABLES 87 3.6 3.7 Free Field Theories 4.1 The Divergence Complex of a Measure 4.2 The Prefactorization Algebra of a Free Field Theory 4.3 Quantum Mechanics and the Weyl Algebra 4.4 Pushforward and Canonical Quantization 4.5 Abelian Chern-Simons Theory 4.6 Another Take on Quantizing Classical Observables 4.7 Correlation Functions 4.8 Translation-Invariant Prefactorization Algebras 4.9 States and Vacua for Translation Invariant Theories 4 5 6 7 89 89 93 106 112 115 124 129 131 139 Holomorphic Field Theories and Vertex Algebras 5.1 Vertex Algebras and Holomorphic Prefactorization Algebras on C 5.2 Holomorphically Translation-Invariant Prefactorization Algebras 5.3 A General Method for Constructing Vertex Algebras 5.4 The βγ System and Vertex Algebras 5.5 Кас-Moody Algebras and Factorization Envelopes 145 PART III 205 FACTORIZATION ALGEBRAS 145 149 157 171 188 Factorization Algebras: Definitions and Constructions 6.1 Factorization Algebras 6.2 Factorization Algebras in Quantum Field Theory 6.3 Variant Definitions of Factorization Algebras 6.4 Locally Constant Factorization Algebras 6.5 Factorization Algebras from Cosheaves 6.6 Factorization Algebras from Local Lie Algebras 207 207 Formal Aspects of Factorization Algebras 7.1 Pushing Forward Factorization Algebras 7.2 Extension from a Basis 232 232 232 215 216 220 225 230
Contents 7.3 7.4 8 Pulling Back Along an Open Immersion Descent Along a Torsor Factorization Algebras: Examples 8.1 Some Examples of Computations 8.2 Abelian Chern-Simons Theory and Quantum Groups ix 240 241 243 243 249 Appendix A Background 273 Appendix В Functional Analysis 310 Appendix C Homological Algebra in Differentiable Vector Spaces 351 Appendix D The Atiyah-Bott Lemma 374 References 377 Index 383 |
| any_adam_object | 1 |
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| discipline | Physik |
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| indexdate | 2024-07-20T06:31:05Z |
| institution | BVB |
| isbn | 9781107163102 |
| language | English |
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| physical | IX, 387 Seiten |
| publishDate | 2017 |
| publishDateSearch | 2017 |
| publishDateSort | 2017 |
| publisher | Cambridge University Press |
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| spelling | Costello, Kevin 1977- Verfasser (DE-588)1020383682 aut Factorization algebras in quantum field theory Volume 1 Factorization algebras in quantum field theory Kevin Costello, Perimeter Institute for Theoretical Physics, Waterloo, Ontario; Owen Gwilliam, Max-Planck-Institut for Mathematics, Bonn, University of Massachusetts, Amherst Cambridge Cambridge University Press 2017 IX, 387 Seiten txt rdacontent n rdamedia nc rdacarrier New mathematical monographs 31 Gwilliam, Owen Verfasser (DE-588)1127755161 aut (DE-604)BV044036120 1 New mathematical monographs 31 (DE-604)BV035420183 31 Digitalisierung UB Regensburg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029443275&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Costello, Kevin 1977- Costello, Kevin 1977- Gwilliam, Owen Gwilliam, Owen Factorization algebras in quantum field theory New mathematical monographs |
| title | Factorization algebras in quantum field theory |
| title_auth | Factorization algebras in quantum field theory |
| title_exact_search | Factorization algebras in quantum field theory |
| title_full | Factorization algebras in quantum field theory Volume 1 Factorization algebras in quantum field theory Kevin Costello, Perimeter Institute for Theoretical Physics, Waterloo, Ontario; Owen Gwilliam, Max-Planck-Institut for Mathematics, Bonn, University of Massachusetts, Amherst |
| title_fullStr | Factorization algebras in quantum field theory Volume 1 Factorization algebras in quantum field theory Kevin Costello, Perimeter Institute for Theoretical Physics, Waterloo, Ontario; Owen Gwilliam, Max-Planck-Institut for Mathematics, Bonn, University of Massachusetts, Amherst |
| title_full_unstemmed | Factorization algebras in quantum field theory Volume 1 Factorization algebras in quantum field theory Kevin Costello, Perimeter Institute for Theoretical Physics, Waterloo, Ontario; Owen Gwilliam, Max-Planck-Institut for Mathematics, Bonn, University of Massachusetts, Amherst |
| title_short | Factorization algebras in quantum field theory |
| title_sort | factorization algebras in quantum field theory factorization algebras in quantum field theory |
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