Higher-order quantum corrections in the presence of an instanton background field

We calculate the ultraviolet divergent part of the two-loop correction to the vacuum energy in the presence of an instanton background field. We verify that the coupling constant and fermion mass, which appear in the semi-classical calculation of the vacuum energy, indeed become 'running' parameters. Among the delicate features of this calculation is the treatment of the zero modes, and in particular the calculation of the corrections to the jacobian corresponding to the change of variables from the zero modes to the collective coordinates. (orig.)