  To account for the interference effects of the Coulomb and exchange
interactions of electrons a new path integral representation of the density
matrix has been developed in the canonical ensemble at finite temperatures. The
developed representation allows to reduce the notorious ``fermionic sign
problem'' in the Monte Carlo simulations of fermionic systems. The obtained
results for pair distribution functions in plasma and uniform electron gas
demonstrate the short-range quantum ordering of electrons associated with
exchange excitons in the literature. This fine physical effect was not observed
earlier in standard path integral Monte Carlo simulations.
