A Relativistic Wave Equation for the Skyrmion

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.