عنوان

Chern-Simons theory and equivariant factorization algebras /

365825338X

9783658253387

3658253371

9783658253370

Chern-Simons theory and equivariant factorization algebras /

[Book]

Corina Keller.

Wiesbaden, Germany :

Springer Spektrum,

2019.

1 online resource (viii, 154 pages) :

illustrations

BestMasters,

2625-3577

Includes bibliographical references.

Intro; Acknowledgement; Contents; 1 Introduction; 1.1 Classical Field Theory and Derived Deformations; 1.2 Factorization Algebras; 1.3 Chern-Simons Theory; 1.4 Overview of this Thesis; 2 Principal Bundles and Gauge Theory; 2.1 Physical Motivation; 2.2 Fiber Bundles; 2.3 Principal Fiber Bundles; 2.4 Connections on Principal Bundles; 2.5 Gauge Transformations; 2.6 The Curvature of a Connection; 3 Differential Graded Algebras; 3.1 Algebras; 3.2 Graded Vector Spaces; 3.3 Chain Complexes; 3.4 Graded Algebras; 3.5 Differential Graded Algebras; 4 L∞-Algebrasand Derived Formal Moduli Problems

4.1 Classical Deformation Theory of Associative Algebras4.2 Differential Graded Lie Algebras and the Maurer-Cartan Equation; 4.3 Formal Description of Classical Deformation Theory; 4.4 Derived Deformation Theory; 5 Factorization Algebras; 5.1 Sheaves and Cosheaves; 5.2 Prefactorization Algebras; 5.3 Factorization Algebras; 6 Observables in U(1) Chern-Simons Theory; 6.1 The Chern-Simons Functional; 6.2 The Moduli Space of Flat Bundles; 6.3 The Derived Formal Moduli Problem for Flat Abelian Bundles; 6.4 Equivariant Factorization Algebras; 6.5 Summary and Outlook; Bibliography; A Category Theory

A.1 Categories and FunctorsA. 2 Natural Transformations; A.3 Limits; A.4 Representables; A.5 Adjunctions; A.6 Comments on Categories with Model Structures; B Simplicial Sets; B.1 Definitions; B.2 Basic Examples; B.3 Simplicial Realization; B.4 Products of Simplicial Sets; B.5 Simplicial Homotopy Theory; B.6 Differential Forms on Simplicial Sets

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Corina Keller studies non-perturbative facets of abelian Chern-Simons theories. This is a refinement of the entirely perturbative approach to classical Chern-Simons theory via homotopy factorization algebras of observables that arise from the associated formal moduli problem describing deformations of flat principal bundles with connections over the spacetime manifold. The author shows that for theories with abelian group structure, this factorization algebra of classical observables comes naturally equipped with an action of the gauge group, which allows to encode non-perturbative effects in the classical observables. Contents Gauge Theory Differential Graded Algebras Differential Graded Lie Algebras and Derived Deformation Theory Factorization Algebras Equivariant Factorization Algebras from Abelian Chern-Simons Theory Target Groups Scientists and students in the field of mathematical physics, theoretical physics and especially mathematics with focus on homotopy theory and homological algebra About the Author Corina Keller currently is a doctoral student in the research group of Prof. Dr. Damien Calaque at the Université Montpellier, France. She is mostly interested in the mathematical study of field theories. Her master?s thesis was supervised by PD Dr. Alessandro Valentino and Prof. Dr. Alberto Cattaneo at Zurich University, Switzerland.

Chern-Simons theory and equivariant factorization algebras.

9783658253370

Factors (Algebra)

Factors (Algebra)

Keller, Corina

20200823183658.0

pn

[Book]

Y