2006/09/17 by Gerald V. Dunne, Jin Hur, Choonkyu Lee
Engineering · Mathematics · Physics and Astronomy · #Action (physics) #Algorithm #Applied mathematics #Computation #Cutoff #Effective action #Instanton #Logarithm #Mathematical analysis #Mathematical physics #Mathematics #Minkowski space #Particle Accelerators and Free-Electron Lasers #Particle physics theoretical and experimental studies #Physics #Quantum Chromodynamics and Particle Interactions #Quantum mechanics #Renormalization #WKB approximation #hep-th
paper · pdf · doi:10.1103/physrevd.74.085025
published as Phys.Rev.D74:085025,2006 · 35 pages
arxiv created 2006/09/17 · openalex publication_date 2006/10/23 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
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.