Radiatively Induced Non Linearity in the Walecka Model

TL;DR

This paper investigates how radiative corrections induce non-linear effects in the Walecka model, enhancing its physical predictions by including vacuum contributions and scale-dependent terms.

Contribution

It introduces a non-perturbative evaluation and renormalization of the effective potential, incorporating vacuum effects that mimic non-linear interactions in the Walecka model.

Findings

Improved predictions of compressibility modulus.

Enhanced effective nucleon mass at saturation.

Inclusion of scale-dependent vacuum contributions.

Abstract

We evaluate the effective potential for the conventional linear Walecka non perturbatively up to one loop. This quantity is then renormalized with a prescription which allows finite vacuum contributions to the three as well as four 1PI Green's functions to survive. These terms, which are absent in the standard relativistic Hartree approximation, have a logarithmic energy scale dependence that can be tuned so as to mimic the effects of phi3 and phi4 type of terms present in the non linear Walecka model improving quantities such as the compressibility modulus and the effective nucleon mass, at saturation, by considering energy scales which are very close to the nucleon mass at vanishing density.