Dunne, Gerald VincentHur, JinLee, Choonkyu2007-01-162007-01-162006Physical Review D, 2006; 7408(8):0850251550-7998http://hdl.handle.net/2440/23579The 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.en©2006 American Physical SocietyBoundary-value-problems; functional determinants; quantum fluctuations; gauge field; canonical-transformations; vacuum polarization; WKB approximation; external fields; operators; equationJournal article002006163210.1103/PHYSREVD.74.0850250002417240001002-s2.0-33750443897