First Course in Topological Field Theory
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A01=Christoph Schweigert
A01=Jurgen Fuchs
A01=Lukas Woike
Author_Christoph Schweigert
Author_Jurgen Fuchs
Author_Lukas Woike
Category=PBP
Category=PHU
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eq_isMigrated=1
eq_nobargain
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forthcoming
Product details
- ISBN 9781470485078
- Publication Date: 30 Jun 2026
- Publisher: American Mathematical Society
- Publication City/Country: US
- Product Form: Paperback
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Topological quantum field theories lie at the intersection of algebra, topology, and quantum field theory. The area is highly active, driven by recent developments in representation theory and topology, as well as developments in theoretical physics, including the study of topological phases of matter and topological symmetries. This book provides an accessible introduction to topological quantum field theories, along with basic notions of category theory - the natural mathematical setting for topological field theories - by describing these theories as a symmetric monoidal functor from a cobordism category to the category of vector spaces.
Using Dijkgraaf–Witten theories as a recurring example, the book introduces key tools such as category theory, Hopf algebras, and tensor categories, providing a solid foundation for students aiming to pursue a more advanced study in quantum topology and related areas.
The book concludes with an outlook connecting the foundational theory to recent developments and current research directions.
The text is intended for advanced undergraduates and beginning graduate students in mathematics and theoretical physics. It is largely self-contained and assumes no specific background beyond standard undergraduate algebra and topology. While some familiarity with basic ideas from quantum theory is helpful, it is not a prerequisite.
Using Dijkgraaf–Witten theories as a recurring example, the book introduces key tools such as category theory, Hopf algebras, and tensor categories, providing a solid foundation for students aiming to pursue a more advanced study in quantum topology and related areas.
The book concludes with an outlook connecting the foundational theory to recent developments and current research directions.
The text is intended for advanced undergraduates and beginning graduate students in mathematics and theoretical physics. It is largely self-contained and assumes no specific background beyond standard undergraduate algebra and topology. While some familiarity with basic ideas from quantum theory is helpful, it is not a prerequisite.
