Heaviside transform of the effective potential in the Gross-Neveu model

TL;DR

This paper introduces a novel approach using Heaviside transformation to approximate the effective potential in the Gross-Neveu model, enabling accurate dynamical mass calculations at finite orders and proving convergence to the exact potential.

Contribution

The paper presents a new method applying Heaviside transform to the effective potential, improving perturbative approximations in the Gross-Neveu model.

Findings

Accurate dynamical mass values obtained at finite orders.

Convergence of the approximants to the exact potential proven.

Small mass expansion of the effective potential achieved.

Abstract

Unconventional way of handling the perturbative series is presented with the help of Heaviside transformation with respect to the mass. We apply Heaviside transform to the effective potential in the massive Gross-Neveu model and carry out perturbative approximation of the massless potential by dealing with the resulting Heaviside function. We find that accurate values of the dynamical mass can be obtained from the Heaviside function already at finite orders where just the several of diagrams are incorporated. We prove that our approximants converges to the exact massless potential in the infinite order. Small mass expansion of the effective potential can be also obtained in our approach.