Coherent functional expansions in quantum field theory

TL;DR

This paper introduces a novel formalism using coherent functional expansions for quantum field theory, offering a potentially divergence-free alternative to traditional perturbation methods, demonstrated on a Bose gas model.

Contribution

It develops a new coherent functional expansion approach that replaces path integrals in quantum field theory, with applications to Bose gases and potential to avoid divergence issues.

Findings

Derives basic identities for the new formalism

Solves a functional equation for Bose gas in weak interactions

Suggests potential to prevent Dyson divergence problem

Abstract

A new formalism is introduced to treat problems in quantum field theory, using coherent functional expansions rather than path integrals. The basic results and identities of this approach are developed. In the case of a Bose gas with point-contact interactions, this leads to a soluble functional equation in the weak interaction limit, where the perturbing term is part of the kinetic energy. This approach has the potential to prevent the Dyson problem of divergence in perturbation theory.