Feynman approximation to integrals with respect to Brownian sheet on Lie groups

Abstract

We consider the Feynman-type approximations to functional integrals over the distribution of the Brownian sheet on a compact connected Lie group M, which give a representation of the integrals over the functional space C([0, 1] × [0, 1], M) as the limit of integrals over the finite-dimensional manifolds M × ⋯ × M. The known approximation formulas for the one-parameter Brownian motion are generalized to the case of the Brownian sheet.