02629nam a22003735a 4500001001100000003001200011005001700023006001900040007001500059008004100074020001800115024002100133040001400154072001700168084003600185100003100221245013500252260008200387300003400469336002600503337002600529338003600555347002400591490004000615506006600655520125700721650003101978650003802009650004002047650004602087650002402133856003202157856006602189114-100601CH-001817-320100601234500.0a fot ||| 0|cr nn mmmmamaa100601e20100601sz fot ||| 0|eng d a978303719586470a10.4171/0862doi ach0018173 7aPBPD2bicssc a57-xxa16-xxa18-xxa81-xx2msc1 aTuraev, Vladimir,eauthor.10aHomotopy Quantum Field Theoryh[electronic resource] :bWith Appendices by Michael Müger and Alexis Virelizier /cVladimir Turaev3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2010 a1 online resource (290 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aEMS Tracts in Mathematics (ETM)v101 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aHomotopy 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.07aAlgebraic topology2bicssc07aManifolds and cell complexes2msc07aAssociative rings and algebras2msc07aCategory theory; homological algebra2msc07aQuantum theory2msc40uhttps://doi.org/10.4171/086423cover imageuhttps://www.ems-ph.org/img/books/turaev_mini.jpg