Partition Function for a System of Interacting Bose-Einstein Particles

It is shown by a rigorous development from first principles that a relatively simple form for the partition function of an imperfect Bose-Einstein gas can be obtained. This form is that of a $3N$-dimensional integral ($N$ being the total number of particles) the integrand of which can be completely determined for any given interparticle interaction provided certain, in general small, many-body quantum mechanical effects are ignored. The final evaluation of the partition function in closed form requires that this integrand be approximated by functions sufficiently tractable that the $3N$-dimensional integral can be performed.