Representations of General Dimension for the Skyrme Model

Abstract

We construct the representations of general dimension for the soliton solution to the $SU(2)$ Skyrme model, and show that at the classical level the dependence on the dimension of the representation ($2j+1$) appears only as an overall factor $j(j+1)(2j+1)$ in the Lagrangian density, which may be absorbed by a rescaling of the parameters. Alternate stabilizing terms in the model will in general have a different $j$-dependence and have to be rescaled accordingly in order to achieve representation independent predictions. In contrast the quantum corrections do depend on the dimension of the representation and in general differ from those obtained in the fundamental representation of $SU(2)$.