Finkelstein-Rubinstein constraints for the Skyrme model with pion masses

TL;DR

This paper extends the calculation of Finkelstein-Rubinstein constraints in the Skyrme model to configurations with pion masses, especially for large baryon numbers where rational map approximations fail, using numerical methods.

Contribution

It introduces a method to compute Finkelstein-Rubinstein constraints for numerically known Skyrme configurations with pion masses, beyond rational map approximations.

Findings

Derived a numerical approach for Finkelstein-Rubinstein constraints

Applied the method to Skyrmions with pion mass terms

Enhanced understanding of quantization conditions for large baryon number Skyrmions

Abstract

The Skyrme model is a classical field theory modelling the strong interaction between atomic nuclei. It has to be quantized in order to compare it to nuclear physics. When the Skyrme model is semi-classically quantized it is important to take the Finkelstein-Rubinstein constraints into account. Recently, a simple formula has been derived to calculate the these constraints for Skyrmions which are well-approximated by rational maps. However, if a pion mass term is included in the model, Skyrmions of sufficiently large baryon number are no longer well-approximated by the rational map ansatz. This paper addresses the question how to calculate Finkelstein-Rubinstein constraints for Skyrme configurations which are only known numerically.