Lectures on Field Theory and Topology - Couverture souple

Freed, Daniel S.

Couverture souple

ISBN 10 : 1470452065 ISBN 13 : 9781470452063

Editeur : American Mathematical Society, 2019

Synopsis

These lectures recount an application of stable homotopy theory to a concrete problem in low energy physics: the classification of special phases of matter. While the joint work of the author and Michael Hopkins is a focal point, a general geometric frame of reference on quantum field theory is emphasized.

Early lectures describe the geometric axiom systems introduced by Graeme Segal and Michael Atiyah in the late 1980s, as well as subsequent extensions. This material provides an entry point for mathematicians to delve into quantum field theory. Classification theorems in low dimensions are proved to illustrate the framework. The later lectures turn to more specialized topics in field theory, including the relationship between invertible field theories and stable homotopy theory, extended unitarity, anomalies, and relativistic free fermion systems. The accompanying mathematical explanations touch upon (higher) category theory, duals to the sphere spectrum, equivariant spectra, differential cohomology, and Dirac operators.

The outcome of computations made using the Adams spectral sequence is presented and compared to results in the condensed matter literature obtained by very different means. The general perspectives and specific applications fuse into a compelling story at the interface of contemporary mathematics and theoretical physics.

A propos du livre

À propos de l'auteur

Daniel S. Freed, University of Texas at Austin, TX.

Détails de l'édition

• Éditeur: American Mathematical Society
• Date d'édition: 2019
• Langue: anglais
• ISBN 10: 1470452065
• ISBN 13: 9781470452063
• Reliure: Broché
• Nombre de pages: 186
• Coordonnées du fabricant: non disponible
• Personne responsable: non disponible