Poisson fields and distribution functions in the statistical mechanics of charged particles

A brief survey of the Poisson analysis on the spaces of tempered distributions is given and the generalized Wick theorem for Poisson fields is formulated. For systems of charged particles, new representations in terms of integrals with respect to the Poisson measure are obtained for distribution functions and diagonal elements of a reduced density matrix; these representations are convenient for investigation of model systems of statistical mechanics by the cluster expansion method. In the quantum case, the Boltzmann, Fermi-Dirac, and Bose-Einstein statistics are studied.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 47, No. 5, pp. 710–719, May, 1995.The author expresses his deep gratitude to A. L. Rebenko for posing the problem and for his attention to the work and to G. F. Us for helpful discussions.This research was partially supported by the International Science Foundation, grant No. UB3000.