Ursell Operators in Statistical Physics II: Microscopic Properties of a Dilute Quantum Gas

(Received 7 April 1995, accepted 20 June 1995)

Abstract
We apply the formalism of Ursell operators, introduced in a previous article, to the calculation of reduced density operators (one and two-body density operators) in a dilute quantum gas; the calculation is not a fugacity expansion and is therefore not limited to low degrees of degeneracy. We obtain quantum corrections for the one-particle density operator as a function of the second Ursell operator. For the two-body density operator, we examine how statistics and interactions combine their effects on the correlations between particles; in particular we discuss in detail how hard cores potentials affect the short range correlations, a non-perturbative effect.