Holomorphic Methods in Mathematical Physics
Brian C. Hall
TL;DR
This paper introduces holomorphic function spaces, focusing on the Segal-Bargmann space and its applications in mathematical physics, including advanced topics like Lie groups and infinite-dimensional analysis.
Contribution
It provides a comprehensive overview of holomorphic methods in mathematical physics, highlighting recent developments and their applications.
Findings
Detailed exposition of the Segal-Bargmann space and transform
Extension to compact Lie groups and infinite-dimensional spaces
Connections between holomorphic functions and quantum physics
Abstract
This set of lecture notes gives an introduction to holomorphic function spaces as used in mathematical physics. The emphasis is on the Segal-Bargmann space and the canonical commutation relations. Later sections describe more advanced topics such as the Segal-Bargmann transform for compact Lie groups and the infinite-dimensional theory.
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Taxonomy
TopicsAdvanced Algebra and Geometry · Algebraic and Geometric Analysis · Advanced Topics in Algebra