Many-Body Problem in Quantum Statistical Mechanics. I. General Formulation

A formulation is given whereby the grand partition function of a many-body system satisfying Bose-Einstein or Fermi-Dirac statistics is expressed in terms of certain $U$ functions defined for the same system with Boltzmann statistics. It is then shown that these $U$ functions can be evaluated in successive approximations in terms of a binary kernel $B$ which can be computed from a solution of the two-body problem. The approach to the limit of infinite volume is studied. The example of a hard sphere interaction is discussed in some detail.