A Relativistic Wave Equation for the Skyrmion

TL;DR

This paper introduces a relativistically invariant wave equation for Skyrmions, predicting particle masses and magnetic moments consistent with known spectra for particles with various spins and isospins.

Contribution

It develops a new relativistic wave equation for Skyrme solitons that accounts for Lorentz and isospin invariance, providing predictions for particle masses and magnetic moments.

Findings

Predicts particle masses matching low angular momentum spectra.

Provides a formula for iso-scalar magnetic moments.

Ensures Lorentz and isospin invariance in the wave equation.

Abstract

We propose a relativistically invariant wave equation for the Skyrme soliton. It is a differential equation on the space $R^{1,3}\times S^3$ which is invariant under the Lorentz group and isospin. The internal variable valued in $SU(2)\approx S^3$ describes the orientation of the soliton. The mass of a particle of spin and isospin both equal to $j={1\over 2},{3\over 2}...$ is predicted to be $M=m\sqrt{1+K_2j(j+1)\over 1+K_1j(j+1)}$ which agrees with the known spectrum for low angular momentum. The iso-scalar magnetic moment is predicted to be $-{K_1\over 4m}{\mathbf \Sigma}$, where ${\mathbf \Sigma}$ is the spin.