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Type: Journal article
Title: Renormalized effective actions in radially symmetric backgrounds: partial wave cutoff method
Author: Dunne, Gerald Vincent
Hur, Jin
Lee, Choonkyu
Citation: Physical Review D, 2006; 7408(8):085025
Publisher: American Physical Society
Issue Date: 2006
ISSN: 1550-7998
School/Discipline: School of Chemistry and Physics : Physics and Mathematical Physics
Statement of
Dunne, Gerald V. ; Hur, Jin ; Lee, Choonkyu
Abstract: 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.
Keywords: Boundary-value-problems; functional determinants; quantum fluctuations; gauge field; canonical-transformations; vacuum polarization; WKB approximation; external fields; operators; equation
Rights: ©2006 American Physical Society
DOI: 10.1103/PHYSREVD.74.085025
Appears in Collections:Physics publications

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