Homotopy Quantum Field Theory (EMS Tracts in Mathematics) [Hardcover]

Vladimir Turaev (Author)

Book Description

Publication Date: May 15, 2010 | Series: Ems Tracts in Mathematics (Book 10)

Homotopy 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. A publication of the European Mathematical Society (EMS). Distributed within the Americas by the American Mathematical Society.

Product Details

• Hardcover: 290 pages
• Publisher: European Mathematical Society (May 15, 2010)
• Language: English
• ISBN-10: 3037190868
• ISBN-13: 978-3037190869
• Product Dimensions: 9.6 x 7 x 1 inches
• Shipping Weight: 1.6 pounds (View shipping rates and policies)
• Amazon Best Sellers Rank: #3,176,543 in Books (See Top 100 in Books)

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