Factorization Algebras in Quantum Field Theory: Volume 2

This second volume shows how factorization algebras arise from interacting field theories, both classical and quantum.

Ideal for researchers and graduate students at the interface between mathematics and physics, this text develops quantum field theory from the ground up using a rich mix of modern mathematics. It provides a unified approach to deformation quantization, Hochschild homology, vertex algebras, conformal field theory, quantum groups, and gauge theory.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.