Note on the one-dimensional gas of impenetrable point-particle bosons

Abstract

A one-dimensional gas of impenetrable point-particle bosons is considered. An exact expression for the one-particle density matrix is derived in terms of the Fredholm determinant and resolvent of a certain simple kernel. It is proved that for large r, the density matrix is bounded by const X r-4/x2, and that this implies the absence of a generalized Bose-Einstein condensation, contrary to a recent approximate calculation by Girardeau, who first defined such a condensation.