Cluster expansion and the Feynman path-integral

We develop an approach of calculating the many-body path integral based on the idea of linked cluster expansion. We will discuss the diagrammatic rules for calculating the free-energy and the pair distribution function. The calculated pair-distribution function for distinguishable particles interacting with Lennard-Jones potential, in various attempted schemes of approximation and partial resummations of the diagrammatic series, compares very well with the results of path integral Monte Carlo simulation. Our method can be extended to the case of identical particles and in particular to the case of the many-fermion problem where the quantum Monte Carlo method is plagued by the infamous ``sign''-problem.