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: IntroductionCategory TheoryTreesColored OperadsConstructions on OperadsBoardman-Vogt Construction of OperadsAlgebras over the Boardman-Vogt ConstructionAlgebraic Quantum Field TheoriesHomotopy Algebraic Quantum Field TheoriesPrefactorization AlgebrasHomotopy Prefactorization AlgebrasComparing 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
