Homotopy of Rational Maps and the Quantization of Skyrmions

TL;DR

This paper develops a homotopy-theoretic method to compute Finkelstein-Rubinstein constraints directly from rational maps, enabling quantization of the Skyrme model for nuclei up to 22 nucleons and comparison with experimental data.

Contribution

It introduces a homotopy-based approach to calculate FR constraints from rational maps, facilitating improved quantization of the Skyrme model.

Findings

Quantized nuclei up to 22 nucleons using the new method.

Results show good agreement with experimental nuclear data.

Provides a systematic way to incorporate topological constraints in nuclear modeling.

Abstract

The Skyrme model is a classical field theory which models 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. The aim of this paper is to show how to calculate these FR constraints directly from the rational map ansatz using basic homotopy theory. We then apply this construction in order to quantize the Skyrme model in the simplest approximation, the zero mode quantization. This is carried out for up to 22 nucleons, and the results are compared to experiment.