1997, Volume 217

The volume contains 8 papers of Russian and foreign authors devoted to important problems in the theory of loop spaces of Lie groups and smooth manifolds. Since there is always a natural action of the diffeomorphism group of a circle on such spaces (by the reparametrization of loops) the study of loop spaces is closely related to the analysis of this group and, more generally, the diffeomorphism groups of compact smooth manifolds. The main topics of the volume are: differential geometry (symplectic and Kahler geometry, in particular) of loop spaces, geometric and stochastic quantization of loop spaces, quasi-invariant measures on diffeomorphism groups and other infinite-dimensional Lie groups.
For scientists, post-graduates and students working in mathematical physics, differential geometry, functional and complex analysis, probability theory.

ISBN: 5-02-002431-7
UDC: 517.9