The Strong-Coupling Expansion and the Ultra-local Approximation in Field Theory

TL;DR

This paper explores the strong-coupling expansion in Euclidean field theory, focusing on the ultra-local approximation, and discusses methods to control divergences and compute the renormalized vacuum energy.

Contribution

It introduces a novel approach to the strong-coupling expansion using the ultra-local approximation and lattice regularization, extending calculations beyond one-loop level.

Findings

Analyzed the analytic structure of generating functions in the complex coupling plane.

Developed a lattice-based regularization method for ultra-local generating functionals.

Demonstrated computation of the renormalized vacuum energy beyond one-loop.

Abstract

We discuss the strong-coupling expansion in Euclidean field theory. In a formal representation for the Schwinger functional, we treat the off-diagonal terms of the Gaussian factor as a perturbation about the remaining terms of the functional integral. We first study the strong-coupling expansion in the \phi^4 theory and also quantum electrodynamics. Assuming the ultra-local approximation, we examine the analytic structure of the zero-dimensional generating functions in the complex coupling constants plane. Second, we discuss the ultra-local generating functional in two idealized field theory models. To control the divergences of the strong-coupling perturbative expansion two different steps are used. First, we introduce a lattice structure to give meaning to the ultra-local generating functional. Using an analytic regularization procedure we discuss briefly how it is possible to obtain a renormalized Schwinger functional associated with these scalar models, going beyond the ultra-local approximation. Using the strong-coupling perturbative expansion we show how it is possible to compute the renormalized vacuum energy of a self-interacting scalar field, going beyond the one-loop level.