Geodesic
Equivalence of the Brownian and energy representations
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 22, Tome 441 (2015), pp. 17-44

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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. 
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     author = {S. Albeverio and B. K. Driver and M. Gordina and A. M. Vershik},
     title = {Equivalence of the {Brownian} and energy representations},
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     pages = {17--44},
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     volume = {441},
     year = {2015},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2015_441_a3/}
}
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S. Albeverio; B. K. Driver; M. Gordina; A. M. Vershik. Equivalence of the Brownian and energy representations. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 22, Tome 441 (2015), pp. 17-44. http://geodesic.mathdoc.fr/item/ZNSL_2015_441_a3/