Holomorphic Methods in Mathematical 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.

Final version

References in corpus (3)

• Toeplitz Quantization of Kähler Manifolds and $gl(N)$ $N\to \infty$
• Legendrian Distributions with Applications to Poincaré Series
• Coherent states, Yang-Mills theory, and reduction

Cited by in corpus (9)

• Quantum mechanics of null polygonal Wilson loops
• Conformal symmetry of the Lange-Neubert evolution equation
• Holomorphic representation of quantum computations
• Quantum Machine Learning using Gaussian Processes with Performant Quantum Kernels
• Conformal constraints for anomalous dimensions of leading twist operators
• Micro-local analysis of contact Anosov flows and band structure of the Ruelle spectrum
• Aharonov-Bohm effect in phase space
• Path Integrals on Euclidean Space Forms
• Fock space on ${\mathbb{C}}^{\infty }$ and Bose-Fock space