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Equivariant cohomology, Fock space and loop groups. (English) Zbl 1100.58015

Summary: Equivariant de Rham cohomology is extended to the infinite-dimensional setting of a loop subgroup acting on a loop group, using Hida supersymmetric Fock space for the Weil algebra and Malliavin test forms on the loop group. The Mathai–Quillen isomorphism (in the BRST formalism of Kalkman) is defined so that the equivalence of various models of the equivariant de Rham cohomology can be established.

MSC:

58J65 Diffusion processes and stochastic analysis on manifolds
60J65 Brownian motion
81T60 Supersymmetric field theories in quantum mechanics
22E70 Applications of Lie groups to the sciences; explicit representations
55N25 Homology with local coefficients, equivariant cohomology
22E67 Loop groups and related constructions, group-theoretic treatment
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