Geodesic
Integral Models of Representations of Current Groups
Funkcionalʹnyj analiz i ego priloženiâ, Tome 42 (2008) no. 1, pp. 22-32

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We suggest a new construction of nonlocal representations of the current group. Instead of the Fock space, which is usually used in this situation, we consider the direct integral of countable tensor products of representations over the trajectories of some stochastic process. The construction substantially uses the invariance of the so-called infinite-dimensional Lebesgue measure.
Keywords: current group, summable representation, integral of tensor products. 
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     title = {Integral {Models} of {Representations} of {Current} {Groups}},
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A. M. Vershik; M. I. Graev. Integral Models of Representations of Current Groups. Funkcionalʹnyj analiz i ego priloženiâ, Tome 42 (2008) no. 1, pp. 22-32. http://geodesic.mathdoc.fr/item/FAA_2008_42_1_a1/