Harmonic analysis with respect to heat kernel measure

Details Harmonic analysis with respect to heat kernel measure Harmonic analysis with respect to heat kernel measure

2000-06-07

arxiv.org/abs/quant-ph/0006037v1

Bull. (N.S.) Amer. Math. Soc., Vol. 38 (2001), 43-78

Physics

Quantum Physics

Scientific paper

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.

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