Reduced Density Matrices of Quantum Gases. I. Limit of Infinite Volume

Abstract

The reduced density matrices for quantum gases are studied by Banach space techniques. For suitably restricted interactions, they are shown to be analytic functions of the activity. As the volume of the system becomes infinite, they tend in some sense to well‐defined limits for which the same analyticity properties hold. As a consequence, the virial expansion is shown to be convergent in a neighborhood of the origin.