A practical method in calculating one loop quantum fluctuations to the energy of the non-topological soliton

TL;DR

This paper presents a practical numerical method for calculating one-loop quantum corrections to the energy of non-topological solitons, focusing on the Friedberg-Lee model, by summing discrete and continuum spectra and applying renormalization.

Contribution

It introduces an efficient numerical approach to compute quantum effects in soliton models, including phase shift calculation and divergence removal.

Findings

Successfully computed quantum corrections for the Friedberg-Lee soliton.

Demonstrated an efficient numerical method for phase shift calculation.

Validated the renormalization procedure for removing divergences.

Abstract

I have used a practical method to calculate the one-loop quantum correction to the energy of the non-topological soliton in Friedberg-Lee model. The quantum effects which come from the quarks of the Dirac sea scattering with the soliton bag are calculated by a summation of the discrete and continuum energy spectrum of the Dirac equation in the background field of soliton. The phase shift of the continuum spectrum is numerically calculated in an efficient way and all the divergences are removed by the same renormalization procedure.