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 $j=\frac{1}{2},\frac{3}{2}...$ is predicted to be $M=m\sqrt{\frac{1+K_{2}j(j+1)}{1+K_{1}j(j+1)}}$ which agrees with the known spectrum for low angular momentum. The iso-scalar magnetic moment is predicted to be $-\frac{K_1}{4m}\mathbf{\Sigma }$, where $\mathbf{\Sigma }$ is the spin.