Factorization Algebras in Quantum Field Theory

Factorization algebras are local-to-global objects that organize complicated information, similar to sheaves in geometry. They are developed in depth in this set, with examples in field theory, such as recovering vertex algebras and quantum groups from interacting field theories.

Format: Mixed media product
Length: 774 pages
Publication date: 30 September 2022
Publisher: Cambridge University Press

Factorization algebras are remarkable objects that serve as both local and global tools in classical and quantum field theory,resembling the role of sheaves in geometry. These algebras possess the remarkable ability to efficiently organize complex information,making them invaluable in understanding intricate mathematical structures. Their local structure encompasses a wide range of examples, including associative and vertex algebras,where their global structure encompasses the fascinating concepts of Hochschild homology and conformal blocks.

In the first volume of this comprehensive set, the authors delve into the theory of factorization algebras in great detail, showcasing their applications in field theory. They illustrate how factorization algebras can be used to recover vertex algebras from chiral conformal field theories and quantum groups from Abelian Chern–Simons theories. By exploring these examples, the authors provide a deep understanding of the power and versatility of factorization algebras.

In the second volume, the authors take the theory further by demonstrating how factorization algebras emerge from interacting field theories, both classical and quantum. They show how these algebras encode essential information such as operator product expansions, Noether currents, and anomalies, which are crucial in understanding the underlying physics of various physical systems. Through their meticulous analysis and clear explanations, the authors make the complex world of factorization algebras accessible to a wide audience, including both mathematicians and physicists.

Factorization algebras are truly remarkable objects that have revolutionized our understanding of field theory and mathematics in general. With their ability to organize and interpret complex information, these algebras continue to inspire research and advance our knowledge of the fundamental laws of nature. This set of two volumes is a valuable resource for anyone interested in delving into the world of factorization algebras and their applications.

ISBN-13: 9781009006163