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Homotopical Quantum Field Theory (eBook)

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  • 69,689 Words
  • 312 Pages

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.

Contents:
  • Introduction
  • Category Theory
  • Trees
  • Colored Operads
  • Constructions on Operads
  • 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
  • Comparing Prefactorization Algebras and AQFT

Readership: Graduate students, mathematicians, mathematical physicists.Algebraic Quantum Field Theory;Prefactorization Algebra;Causality Axiom;Time-Slice Axiom;Operad;Tree;Boardman-Vogt Construction;Adjunction;Homotopy Coherent Diagram;A-Infinity Algebra;E-Infinity Algebra;E-Infinity Module00

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.

Contents:
  • Introduction
  • Category Theory
  • Trees
  • Colored Operads
  • Constructions on Operads
  • 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
  • Comparing Prefactorization Algebras and AQFT

Readership: Graduate students, mathematicians, mathematical physicists.Algebraic Quantum Field Theory;Prefactorization Algebra;Causality Axiom;Time-Slice Axiom;Operad;Tree;Boardman-Vogt Construction;Adjunction;Homotopy Coherent Diagram;A-Infinity Algebra;E-Infinity Algebra;E-Infinity Module00


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