Failure of the derivative expansion for studying stability of the baryon as a chiral soliton

Abstract

We investigate whether the terms in the derivative expansion up to and including (ϖφ) 6 provide a useful local approximation to the one fermion loop effective action of the SU(2) chiral model, for the purpose of discussing soliton stability. By comparing the contribution of these terms to the static energy with the exact evaluation of the complete one-loop (Casimir) energy, we conclude that the derivative expansion does not provide a useful approximation for discussing stability of the soliton at sizes relevant to nucleon physics.