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.

‘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 Source: Choice Connect

‘… perfectly suitable for self-study by an interested scholar with little to almost no previous exposure to factorization algebras, or for use as a reference text for a lecture series on the subject.’

Domenico Fiorenza Source: MathSciNet