Factorization Algebras in Quantum Field Theory: Volume 2

Description

Factorization algebras are local-to-global objects that play a role in classical and quantum field theory that is similar to the role of sheaves in geometry: they conveniently organize complicated information. Their local structure encompasses examples like associative and vertex algebras; in these examples, their global structure encompasses Hochschild homology and conformal blocks. In this second volume, the authors show how factorization algebras arise from interacting field theories, both classical and quantum, and how they encode essential information such as operator product expansions, Noether currents, and anomalies. Along with a systematic reworking of the Batalin-Vilkovisky formalism via derived geometry and factorization algebras, this book offers concrete examples from physics, ranging from angular momentum and Virasoro symmetries to a five-dimensional gauge theory.

Kevin Costello is Krembil William Rowan Hamilton Chair in Theoretical Physics at the Perimeter Institute for Theoretical Physics, Waterloo, Canada. He is an honorary member of the Royal Irish Academy and a Fellow of the Royal Society. He has won several awards, including the Berwick Prize of the London Mathematical Society (2017) and the Eisenbud Prize of the American Mathematical Society (2020). Owen Gwilliam is Assistant Professor in the Department of Mathematics and Statistics at the University of Massachusetts, Amherst.

'The central achievement of the book is in its development of a formalism that leads to classical and quantum versions of Noether's theorem, itself a familiar topic in physics, using the language of factorization algebras ... Institutions employing mathematicians and theoretical physicists actively working in this area should acquire the book ... Recommended.' M. C. Ogilvie, Choice Connect