  The computation of the one-loop effective action in a radially symmetric
background can be reduced to a sum over partial-wave contributions, each of
which is the logarithm of an appropriate one-dimensional radial determinant.
While these individual radial determinants can be evaluated simply and
efficiently using the Gel'fand-Yaglom method, the sum over all partial-wave
contributions diverges. A renormalization procedure is needed to unambiguously
define the finite renormalized effective action. Here we use a combination of
the Schwinger proper-time method, and a resummed uniform DeWitt expansion. This
provides a more elegant technique for extracting the large partial-wave
contribution, compared to the higher order radial WKB approach which had been
used in previous work. We illustrate the general method with a complete
analysis of the scalar one-loop effective action in a class of radially
separable SU(2) Yang-Mills background fields. We also show that this method can
be applied to the case where the background gauge fields have asymptotic limits
appropriate to uniform field strengths, such as for example in the Minkowski
solution, which describes an instanton immersed in a constant background.
Detailed numerical results will be presented in a sequel.
