A formally exact field theory for classical systems at equilibrium

TL;DR

This paper develops a formally exact statistical field theory for classical fluids, integrating concepts from quantum field theory to accurately describe equilibrium properties and particle indiscernibility.

Contribution

It introduces a novel field-theoretic Hamiltonian for classical fluids that incorporates particle indiscernibility and maps onto standard statistical mechanics via Mayer expansion.

Findings

Established a mapping between the field theory and Mayer function expansion

Demonstrated the approach's validity on chemical potential and interfacial properties

Presented a diagrammatic expansion and renormalization of the Hamiltonian

Abstract

We propose a formally exact statistical field theory for describing classical fluids with ingredients similar to those introduced in quantum field theory. We consider the following essential and related problems : i) how to find the correct field functional (Hamiltonian) which determines the partition function, ii) how to introduce in a field theory the equivalent of the indiscernibility of particles, iii) how to test the validity of this approach. We can use a simple Hamiltonian in which a local functional transposes, in terms of fields, the equivalent of the indiscernibility of particles. The diagrammatic expansion and the renormalization of this term is presented. This corresponds to a non standard problem in Feynman expansion and requires a careful investigation. Then a non-local term associated with an interaction pair potential is introduced in the Hamiltonian. It has been shown that there exists a mapping between this approach and the standard statistical mechanics given in terms of Mayer function expansion. We show on three properties (the chemical potential, the so-called contact theorem and the interfacial properties) that in the field theory the correlations are shifted on non usual quantities. Some perspectives of the theory are given.