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E-grāmata: Homotopical Quantum Field Theory

(The Ohio State Univ At Newark, Usa)
  • Formāts: 312 pages
  • Izdošanas datums: 11-Nov-2019
  • Izdevniecība: World Scientific Publishing Co Pte Ltd
  • Valoda: eng
  • ISBN-13: 9789811212871
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Homotopical Quantum Field TheoryPalielināt
  • Formāts: 312 pages
  • Izdošanas datums: 11-Nov-2019
  • Izdevniecība: World Scientific Publishing Co Pte Ltd
  • Valoda: eng
  • ISBN-13: 9789811212871
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"This book provides a general and powerful definition of homotopy algebraic quantum field theory and homotopy prefactorization algebra using a new coend definition of the Boardman-Vogt construction for a colored operad. All of their homotopy coherent structures are explained in details, along with a comparison between the two approaches at the operad level. With chapters on basic category theory, trees, and operads, this book is self-contained and is accessible to graduate students"--

Using a new coend definition of the Boardman-Vogt construction of a colored operad, Yau defines homotopy algebraic quantum field theories and homotopy prefactorization algebras, and investigates their homotopy coherent structures. The topics are category theory, trees, colored operads, constructions on operads, the Boardman-Vogt construction of operads, algebras over the Boardman-Vogt construction, algebraic quantum field theories, homotopy algebraic quantum field theories, prefactorization algebras, homotopy prefactorization algebras, and comparing prefactorization algebras and algebraic quantum field theories. Annotation ©2020 Ringgold, Inc., Portland, OR (protoview.com)

This book provides a general and powerful definition of homotopy algebraic quantum field theory and homotopy prefactorization algebra using a new coend definition of the Boardman-Vogt construction for a colored operad. All of their homotopy coherent structures are explained in details, along with a comparison between the two approaches at the operad level. With chapters on basic category theory, trees, and operads, this book is self-contained and is accessible to graduate students.

Preface vii
1 Introduction
1(10)
1.1 Algebraic Quantum Field Theory
1(2)
1.2 Homotopy Algebraic Quantum Field Theory
3(2)
1.3 Homotopy Prefactorization Algebra
5(2)
1.4 Comparison
7(1)
1.5 Organization
8(3)
2 Category Theory
11(28)
2.1 Basics of Categories
11(3)
2.2 Examples of Categories
14(4)
2.3 Limits and Colimits
18(4)
2.4 Adjoint Functors
22(2)
2.5 Symmetric Monoidal Categories
24(6)
2.6 Monoids
30(3)
2.7 Monads
33(2)
2.8 Localization
35(4)
3 Trees
39(36)
3.1 Graphs
39(6)
3.2 Tree Substitution
45(4)
3.3 Grafting
49(4)
4 Colored Operads
53(1)
4.1 Operads as Monoids
53(3)
4.2 Operads in Terms of Generating Operations
56(3)
4.3 Operads in Terms of Partial Compositions
59(2)
4.4 Operads in Terms of Trees
61(6)
4.5 Algebras over Operads
67(8)
5 Constructions on Operads
75(22)
5.1 Change-of-Operad Adjunctions
75(4)
5.2 Model Category Structures
79(5)
5.3 Changing the Base Categories
84(1)
5.4 Localizations of Operads
85(7)
5.5 Algebras over Localized Operads
92(5)
6 Boardman-Vogt Construction of Operads
97(26)
6.1 Overview
97(1)
6.2 Commutative Segments
98(4)
6.3 Coend Definition of the BV Construction
102(5)
6.4 Augmentation
107(5)
6.5 Homotopy Morita Equivalence
112(3)
6.6 Filtration
115(8)
7 Algebras over the Boardman-Vogt Construction
123(34)
7.1 Overview
123(1)
7.2 Coherence Theorem
124(4)
7.3 Homotopy Coherent Diagrams
128(6)
7.4 Homotopy Inverses
134(2)
7.5 A∞-Algebras
136(7)
7.6 Eco-Algebras
143(4)
7.7 Homotopy Coherent Diagrams of A∞-Algebras
147(5)
7.8 Homotopy Coherent Diagrams of E∞-Algebras
152(5)
8 Algebraic Quantum Field Theories
157(22)
8.1 From Haag-Kastler Axioms to Operads
157(2)
8.2 AQFT as Functors
159(3)
8.3 AQFT as Operad Algebras
162(6)
8.4 Examples of AQFT
168(9)
8.5 Homotopical Properties
177(2)
9 Homotopy Algebraic Quantum Field Theories
179(22)
9.1 Overview
179(2)
9.2 Homotopy AQFT as Operad Algebras
181(2)
9.3 Examples of Homotopy AQFT
183(2)
9.4 Coherence Theorem
185(2)
9.5 Homotopy Causality Axiom
187(2)
9.6 Homotopy Coherent Diagrams
189(2)
9.7 Homotopy Time-Slice Axiom
191(3)
9.8 Objectwise A∞-Algebra
194(1)
9.9 Homotopy Coherent Diagrams of A∞-Algebras
195(6)
10 Prefactorization Algebras
201(28)
10.1 Costello-Gwilliam Prefactorization Algebras
201(2)
10.2 Configured Categories
203(4)
10.3 Prefactorization Algebras as Operad Algebras
207(5)
10.4 Pointed Diagram Structure
212(4)
10.5 Commutative Monoid Structure
216(2)
10.6 Diagrams of Modules over a Commutative Monoid
218(2)
10.7 Diagrams of Commutative Monoids
220(2)
10.8 Configured and Homotopy Morita Equivalences
222(7)
11 Homotopy Prefactorization Algebras
229(30)
11.1 Overview
229(1)
11.2 Homotopy Prefactorization Algebras as Operad Algebras
230(3)
11.3 Examples
233(4)
11.4 Coherence Theorem
237(3)
11.5 Homotopy Coherent Pointed Diagrams
240(4)
11.6 Homotopy Time-Slice Axiom
244(2)
11.7 E∞-Algebra Structure
246(2)
11.8 Objectwise E∞-Module
248(4)
11.9 Homotopy Coherent Diagrams of E∞-Modules
252(4)
11.10 Homotopy Coherent Diagrams of E∞-Algebras
256(3)
12 Comparing Prefactorization Algebras and AQFT
259(22)
12.1 Orthogonal Categories as Configured Categories
260(2)
12.2 Configured Categories to Orthogonal Categories
262(3)
12.3 Comparison Adjunctions
265(5)
12.4 Examples of Comparison
270(4)
12.5 Prefactorization Algebras from AQFT
274(7)
List of Notations 281(6)
Bibliography 287(4)
Index 291
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