Homotopical quantum field theory

✍ Scribed by Yau, Donald

• Publisher: World Scientific Publishing
• Year: 2020
• Tongue: English
• Leaves: 312
• Category: Library

✦ Table of Contents

Preface......Page 9
Contents......Page 11
1.1 Algebraic Quantum Field Theory......Page 15
1.2 Homotopy Algebraic Quantum Field Theory......Page 17
1.3 Homotopy Prefactorization Algebra......Page 19
1.4 Comparison......Page 21
1.5 Organization......Page 22
2.1 Basics of Categories Definition......Page 25
2.2 Examples of Categories......Page 28
2.3 Limits and Colimits Definition 2.3.1.......Page 32
2.4 Adjoint Functors......Page 36
2.5 Symmetric Monoidal Categories......Page 38
2.6 Monoids......Page 44
2.7 Monads Definition......Page 47
2.8 Localization......Page 49
Theorem 2.8.3.......Page 50
3.1 Graphs......Page 53
3.2 Tree Substitution......Page 59
3.3 Grafting......Page 63
4.1 Operads as Monoids......Page 67
4.2 Operads in Terms of Generating Operations......Page 70
4.3 Operads in Terms of Partial Compositions......Page 73
4.4 Operads in Terms of Trees......Page 75
4.5 Algebras over Operads......Page 81
5.1 Change-of-Operad Adjunctions......Page 89
5.2 Model Category Structures......Page 93
5.3 Changing the Base Categories......Page 98
5.4 Localizations of Operads......Page 99
5.5 Algebras over Localized Operads......Page 106
6.1 Overview......Page 111
6.2 Commutative Segments......Page 112
6.3 Coend Definition of the BV Construction......Page 116
6.4 Augmentation......Page 121
6.5 Homotopy Morita Equivalence......Page 126
6.6 Filtration......Page 129
7.1 Overview......Page 137
7.2 Coherence Theorem......Page 138
7.3 Homotopy Coherent Diagrams......Page 142
7.4 Homotopy Inverses......Page 148
7.5 Aª-Algebras......Page 151
7.6 Eª-Algebras......Page 157
7.7 Homotopy Coherent Diagrams of Aª-Algebras......Page 161
7.8 Homotopy Coherent Diagrams of Eª-Algebras......Page 166
8.1 From Haag-Kastler Axioms to Operads......Page 171
8.2 AQFT as Functors......Page 173
8.3 AQFT as Operad Algebras......Page 176
8.4 Examples of AQFT......Page 182
8.5 Homotopical Properties......Page 191
9.1 Overview......Page 193
9.2 Homotopy AQFT as Operad Algebras......Page 195
9.3 Examples of Homotopy AQFT......Page 197
9.4 Coherence Theorem......Page 199
9.5 Homotopy Causality Axiom......Page 201
9.6 Homotopy Coherent Diagrams......Page 203
9.7 Homotopy Time-Slice Axiom......Page 205
9.8 Objectwise......Page 208
9.9 Homotopy Coherent Diagrams of......Page 209
10.1 Costello-Gwilliam Prefactorization Algebras......Page 215
10.2 Configured Categories......Page 217
10.3 Prefactorization Algebras as Operad Algebras......Page 221
10.4 Pointed Diagram Structure......Page 226
10.5 Commutative Monoid Structure......Page 230
10.6 Diagrams of Modules over a Commutative Monoid......Page 232
10.7 Diagrams of Commutative Monoids......Page 234
10.8 Configured and Homotopy Morita Equivalences......Page 236
11.1 Overview......Page 243
11.2 Homotopy Prefactorization Algebras as Operad Algebras......Page 244
11.3 Examples......Page 247
11.4 Coherence Theorem......Page 251
11.5 Homotopy Coherent Pointed Diagrams......Page 254
11.6 Homotopy Time-Slice Axiom......Page 258
11.7 Eª-Algebra Structure......Page 260
11.8 Objectwise......Page 262
11.9 Homotopy Coherent Diagrams of......Page 266
11.10 Homotopy Coherent Diagrams of Eª-Algebras......Page 270
12. Comparing Prefactorization Algebras and AQFT......Page 273
12.1 Orthogonal Categories as Configured Categories......Page 274
12.2 Configured Categories to Orthogonal Categories......Page 276
12.3 Comparison Adjunctions......Page 279
12.4 Examples of Comparison......Page 284
12.5 Prefactorization Algebras from AQFT......Page 288
Notation Page Description Chapter 2......Page 295
Chapter 3......Page 296
Chapter 4......Page 297
Chapter 7......Page 298
Chapter 10......Page 299
Chapter 12......Page 300
Bibliography......Page 301
Index......Page 305

✦ Subjects

Homotopy theory;Quantum field theory--Mathematics;Quantum field theory -- Mathematics