02761nam 22004575a 450 991015193200332120250513220857.03-03719-586-X10.4171/086(CKB)3710000000953855(CH-001817-3)114-100601(PPN)178155756(EXLCZ)99371000000095385520100601j20100601 fy 0engurnn|mmmmamaatxtrdacontentcrdamediacrrdacarrierHomotopy Quantum Field Theory With Appendices by Michael Müger and Alexis Virelizier /Vladimir TuraevZuerich, Switzerland European Mathematical Society Publishing House20101 online resource (290 pages)EMS Tracts in Mathematics (ETM)10Homotopy Quantum Field Theory (HQFT) is a branch of Topological Quantum Field Theory founded by E. Witten and M. Atiyah. It applies ideas from theoretical physics to study principal bundles over manifolds and, more generally, homotopy classes of maps from manifolds to a fixed target space. This book is the first systematic exposition of Homotopy Quantum Field Theory. It starts with a formal definition of an HQFT and provides examples of HQFTs in all dimensions. The main body of the text is focused on 2-dimensional and 3-dimensional HQFTs. A study of these HQFTs leads to new algebraic objects: crossed Frobenius group-algebras, crossed ribbon group-categories, and Hopf group-coalgebras. These notions and their connections with HQFTs are discussed in detail. The text ends with several appendices including an outline of recent developments and a list of open problems. Three appendices by M. Müger and A. Virelizier summarize their work in this area. The book is addressed to mathematicians, theoretical physicists, and graduate students interested in topological aspects of quantum field theory. The exposition is self-contained and well suited for a one-semester graduate course. Prerequisites include only basics of algebra and topology.Algebraic topologybicsscManifolds and cell complexesmscAssociative rings and algebrasmscCategory theory; homological algebramscQuantum theorymscAlgebraic topologyManifolds and cell complexesAssociative rings and algebrasCategory theory; homological algebraQuantum theory57-xx16-xx18-xx81-xxmscTuraev Vladimir67205ch0018173BOOK9910151932003321Homotopy Quantum Field Theory2564455UNINA