The effective action of a spin 1/2 field in the background of a chiral soliton

We use a recently developed numerical technique in order to evaluate the renormalized effective action of a spin 1/2 field with a chiral mass term, the chiral angle being given by a static hedgehog configuration. The method is based on the use of Euclidean Green's functions. The divergent parts are regularized and renormalized analytically. For the sum over all convergent contributions we obtain an exact expression that can be evaluated numerically. A precarious numerical subtraction of the divergent parts is avoided by making use of integral equations for the partial waves. (orig.)