Limitations of a semiclassical treatment of the Skyrme soliton

Abstract

We discuss a semiclassical approach to the Skyrme model in which the effects from the diagonalization of the collective coordinates are treated in a self-consistent way. We obtain an upper bound on the nucleon-\ensuremath{\Delta} mass difference which is valid if the semiclassical limit is taken with the pion mass parameter held fixed, but is inconsistent with the experimental values of the masses. Because of the interplay of the semiclassical and chiral limits, the approximations break down for sufficiently small pion mass.