Renormalized Effective Actions in Radially Symmetric Backgrounds: Exact Calculations Versus Approximation Methods

Abstract

Our previously-developed calculational method (the partial wave cutoff method) is employed to evaluate explicitly scalar one-loop effective actions in a class of radially symmetric background gauge fields. Our method proves to be particularly effective when it is used in conjunction with a systematic WKB series for the large partial wave contribution to the effective action. By comparing these numerically exact calculations against the predictions based on the large mass expansion and derivative expansion, we discuss the validity ranges of the latter approximation methods.

30 pages, 9 figures, RevTex

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• A Fast Way to Compute Functional Determinants of Radially Symmetric Partial Differential Operators in General Dimensions
• Casimir energies in spherically symmetric background potentials revisited
• Small Mass Expansion of Functional Determinants on the Generalized Cone
• The Derivative Expansion at Small Mass for the Spinor Effective Action
• Full mass range analysis of the QED effective action for an O(2)xO(3) symmetric field
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• Calculation of renormalized fermion effective actions in radially symmetric non-Abelian backgrounds
• New asymptotic techniques for the partial wave cut-off method for calculating the QED one loop effective action