  Our recent method to calculate renormalized functional determinants, the
partial wave cutoff method, is extended for the evaluation of 4-D fermion
one-loop effective action with arbitrary mass in certain types of radially
symmetric, non-Abelian, background gauge fields (including instanton-like and
instanton-antiinstanton-like configurations). A detailed study on functional
determinants for matrix-valued radial differential operators is presented,
explicating both our analytic treatment on the high partial wave contribution
and the application of the generalized Gel'fand-Yaglom formula to determine the
low partial wave contribution. In general, some numerical work is needed for
the low partial wave part. In the massless limit, however, the factorizable
nature of our partial-wave radial differential operators can be exploited to
evaluate semi-analytically even the low partial wave part, and we thus have the
full fermion effective action calculated explicitly in a class of non-Abelian
background gauge fields. With nonzero mass, we also perform necessary numerical
analysis as regards the low partial wave contribution to produce numerically
exact results for the massive effective action. Comparing these against the
results of the large mass expansion, the validity range of the large mass
expansion is addressed. Also studied is the fermion mass dependence of the
effective instanton-antiinstanton interaction.
