A Note on the Resolvent Algebra and Functional Integral Approach to the van Hove Model

Abstract

This paper is a collection of the author's computational notes on the van Hove model and contains no essentially new results. We discuss, from both the operator-algebraic perspective via the Weyl algebra and the resolvent algebra and the functional integral approach, the removal of infrared and ultraviolet cutoffs and the existence of the ground state and $\beta$-KMS states in the case of a point source. In the infinite-volume system at finite temperature, Bose--Einstein condensation can arise.