Harmonic analysis with respect to heat kernel measure
Quantum Physics
2007-05-23 v1 Mathematical Physics
math.MP
Abstract
I review certain results in harmonic analysis for systems whose configuration space is a compact Lie group. The results described involve a heat kernel measure, which plays the same role as a Gaussian measure on Euclidean space. The main constructions are group analogs of the Hermite expansion, the Segal-Bargmann transform, and the Taylor expansion. The results are related to geometric quantization, to stochastic analysis, and to the quantization of 1+1-dimensional Yang-Mills theory.
Cite
@article{arxiv.quant-ph/0006037,
title = {Harmonic analysis with respect to heat kernel measure},
author = {Brian C. Hall},
journal= {arXiv preprint arXiv:quant-ph/0006037},
year = {2007}
}