Equivalence of the Brownian and energy representations
Probability
2015-11-24 v1 Mathematical Physics
math.MP
Representation Theory
Abstract
We consider two unitary representations of the infinite-dimensional groups of smooth paths with values in a compact Lie group. The first representation is induced by quasi-invariance of the Wiener measure, and the second representation is the energy representation. We define these representations and their basic properties, and then we prove that these representations are unitarily equivalent.
Keywords
Cite
@article{arxiv.1511.07378,
title = {Equivalence of the Brownian and energy representations},
author = {Sergio Albeverio and Bruce K. Driver and Maria Gordina and A. M. Vershik},
journal= {arXiv preprint arXiv:1511.07378},
year = {2015}
}
Comments
This an article to be published in "Zapiski Seminarov POMI" dedicated to the memory of Mi.I.Gordin