Nonlinear rigid-body quantization of Skyrmions

TL;DR

This paper explores the nonlinear rigid-body quantization of Skyrmions across various Skyrme models, establishing energy bounds and analyzing spin contributions, with implications for understanding Skyrmion quantum states.

Contribution

It extends rigid-body quantization to general four-derivative Skyrme models, derives new energy bounds, and compares spin contributions across different model limits.

Findings

Standard Skyrme model yields the smallest spin energy contribution.

Established topological energy bounds for multiple Skyrme models.

Analyzed the potential role of spin energy tuning in Skyrmion quantization.

Abstract

We consider rigid-body quantization of the Skyrmion in the most general four-derivative generalization of the Skyrme model with a potential giving pions a mass, as well as in a class of higher-order Skyrme models. We quantize the spin and isospin zeromodes following the results of Pottinger and Rathske. Although one could hope that a one-parameter family of theories could provide a smaller spin contribution to the energy at some point in theory space -- which would be welcome for BPS-type models, we find that the standard Skyrme model limit, with two time derivatives, gives rise to the smallest spin contribution to the energy. We speculate whether this tuning of the spin energy could be useful in the larger picture of quantizing vibrational and light massive modes of the Skyrmions. Finally, we establish a topological energy bound for the Pottinger-Rathske model with potential terms as well as new bounds for higher-order Skyrme models, with and without a potential.