THE FULL DIAGONAL MODEL OF A BOSE-GAS

This paper is the final one in a series in which we investigate some models of an interacting Bose gas using Varadhan's large deviation version of Laplacian asymptotics; in it we study the equilibrium thermodynamics of the full diagonal model of a Bose gas. We obtain a formula expressing the pressure, in the thermodynamic limit, as the supremum of a functional over the space of positive bounded measures. We analyse this formula for a large class of interaction kernels and show that there is a critical temperature below which there is Bose Einstein condensation.