A derivation of the virial expansion with application to Euclidean quantum field theory

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Abstract
In this paper we give a derivation of the virial expansion and some of its generalizations. Our derivation is based on the generating functional which defines a representation of the density operator ρ (x) in a nonrelativistic local current algebra. The virial expansion results from solving a functional differential equation for this quantity. We exploit the well‐known analogy between quantum field theory and classical statistical mechanics to explore the use of the virial expansion in Euclidean quantum field theory. Specifically, we show that the virial expansion can be used to derive Feynman’s rules and to provide a perturbation expansion about a static ultralocal model. The latter is worked out in detail in the case of a free neutral scalar model, and outlined in the case of a λφ4 model.