Fermionic One-Loop Corrections to Soliton Energies in 1+1 Dimensions

TL;DR

This paper presents a clear method for calculating fermionic quantum corrections to soliton energies in 1+1 dimensions, using phase shifts and the Born approximation to ensure unambiguous results.

Contribution

It introduces a robust analytical and numerical approach for computing fermionic corrections to soliton energies, avoiding renormalization ambiguities in 1+1 dimensions.

Findings

Fermionic corrections vary continuously along the interpolation.

Properties of fermionic phase shifts and zero modes are elucidated.

The method is applicable to a range of background configurations.

Abstract

We demonstrate an unambiguous and robust method for computing fermionic corrections to the energies of classical background field configurations. We consider the particular case of a sequence of background field configurations that interpolates continuously between the trivial vacuum and a widely separated soliton/antisoliton pair in 1+1 dimensions. Working in the continuum, we use phase shifts, the Born approximation, and Levinson's theorem to avoid ambiguities of renormalization procedure and boundary conditions. We carry out the calculation analytically at both ends of the interpolation and numerically in between, and show how the relevant physical quantities vary continuously. In the process, we elucidate properties of the fermionic phase shifts and zero modes.