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

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.