Renormalization and effective field theory:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Providence, Rhode Island
American Mathematical Society
[2011]
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| Series: | Mathematical surveys and monographs
Volume 170 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | vii, 251 Seiten Diagramme |
| ISBN: | 9780821852880 0821852884 |
Staff View
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| 245 | 1 | 0 | |a Renormalization and effective field theory |c Kevin Costello |
| 264 | 1 | |a Providence, Rhode Island |b American Mathematical Society |c [2011] | |
| 264 | 4 | |c © 2011 | |
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Record in the Search Index
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| adam_text | Titel: Renormalization and effective field theory
Autor: Costello, Kevin
Jahr: 2011
Contents
Chapter 1. Introduction 1
1. Overview 1
2. Functional integrals in quantum field theory 4
3. Wilsonian low energy theories 6
4. A Wilsonian definition of a quantum field theory 13
5. Locality 13
6. The main theorem 16
7. Renormalizability 19
8. Renormalizable scalar field theories 21
9. Gauge theories 22
10. Observables and correlation functions 27
11. Other approaches to perturbative quantum field theory 27
Acknowledgements 28
Chapter 2. Theories, Lagrangians and counterterms 31
1. Introduction 31
2. The effective interaction and background field functional integrals 32
3. Generalities on Feynman graphs 34
4. Sharp and smooth cut-offs 42
5. Singularities in Feynman graphs 44
6. The geometric interpretation of Feynman graphs 47
7. A definition of a quantum field theory 53
8. An alternative definition 55
9. Extracting the singular part of the weights of Feynman graphs 57
10. Constructing local counterterms 61
11. Proof of the main theorem 67
12. Proof of the parametrix formulation of the main theorem 69
13. Vector-bundle valued field theories 71
14. Field theories on non-compact manifolds 80
Chapter 3. Field theories on M 91
1. Some functional analysis 92
2. The main theorem on Rn 99
3. Vector-bundle valued field theories on Rn 104
4. Holomorphic aspects of theories on Rn 107
Chapter 4. Renormalizability 113
1. The local renormalization group flow 113
2. The Kadanoff-Wilson picture and asymptotic freedom 122
3. Universality 125
4. Calculations in 04 theory 126
5. Proofs of the main theorems 131
6. Generalizations of the main theorems 135
Chapter 5. Gauge symmetry and the Batalin-Vilkovisky formalism 139
1. Introduction 139
2. A crash course in the Batalin-Vilkovisky formalism 141
3. The classical BV formalism in infinite dimensions 155
4. Example: Chern-Simons theory 160
5. Example : Yang-Mills theory 162
6. .D-modules and the classical BV formalism 164
7. BV theories on a compact manifold 170
8. Effective actions 173
9. The quantum master equation 175
10. Homotopies between theories 178
11. Obstruction theory 186
12. BV theories on Rn 189
13. The sheaf of BV theories on a manifold 196
14. Quantizing Chern-Simons theory 203
Chapter 6. Renormalizability of Yang-Mills theory 207
1. Introduction 207
2. First-order Yang-Mills theory 207
3. Equivalence of first-order and second-order formulations 210
4. Gauge fixing 213
5. Renormalizability 214
6. Universality 217
7. Cohomology calculations 218
Appendix 1: Asymptotics of graph integrals 227
1. Generalized Laplacians 227
2. PolydifFerential operators 229
3. Periods 229
4. Integrals attached to graphs 230
5. Proof of Theorem 4.0.2 233
Appendix 2 : Nuclear spaces 243
1. Basic definitions 243
2. Examples 244
3. Subcategories 245
4. Tensor products of nuclear spaces from geometry 247
5. Algebras of formal power series on nuclear Frechet spaces 247
Bibliography 249
|
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| illustrated | Not Illustrated |
| indexdate | 2024-07-09T23:22:46Z |
| institution | BVB |
| isbn | 9780821852880 0821852884 |
| language | English |
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| physical | vii, 251 Seiten Diagramme |
| publishDate | 2011 |
| publishDateSearch | 2011 |
| publishDateSort | 2011 |
| publisher | American Mathematical Society |
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| series | Mathematical surveys and monographs |
| series2 | Mathematical surveys and monographs |
| spelling | Costello, Kevin 1977- Verfasser (DE-588)1020383682 aut Renormalization and effective field theory Kevin Costello Providence, Rhode Island American Mathematical Society [2011] © 2011 vii, 251 Seiten Diagramme txt rdacontent n rdamedia nc rdacarrier Mathematical surveys and monographs Volume 170 Renormierung (DE-588)4128419-7 gnd rswk-swf Quantenfeldtheorie (DE-588)4047984-5 gnd rswk-swf Quantenfeldtheorie (DE-588)4047984-5 s Renormierung (DE-588)4128419-7 s DE-604 Erscheint auch als Online-Ausgabe 978-1-4704-1397-2 Mathematical surveys and monographs Volume 170 (DE-604)BV000018014 170 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=022520584&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Costello, Kevin 1977- Renormalization and effective field theory Mathematical surveys and monographs Renormierung (DE-588)4128419-7 gnd Quantenfeldtheorie (DE-588)4047984-5 gnd |
| subject_GND | (DE-588)4128419-7 (DE-588)4047984-5 |
| title | Renormalization and effective field theory |
| title_auth | Renormalization and effective field theory |
| title_exact_search | Renormalization and effective field theory |
| title_full | Renormalization and effective field theory Kevin Costello |
| title_fullStr | Renormalization and effective field theory Kevin Costello |
| title_full_unstemmed | Renormalization and effective field theory Kevin Costello |
| title_short | Renormalization and effective field theory |
| title_sort | renormalization and effective field theory |
| topic | Renormierung (DE-588)4128419-7 gnd Quantenfeldtheorie (DE-588)4047984-5 gnd |
| topic_facet | Renormierung Quantenfeldtheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=022520584&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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