A Fast Way to Compute Functional Determinants of Radially Symmetric Partial Differential Operators in General Dimensions

Abstract

Recently the partial wave cutoff method was developed as a new calculational scheme for a functional determinant of quantum field theory in radial backgrounds. For the contribution given by an infinite sum of large partial waves, we derive explicitly radial WKB series in the angular momentum cutoff for $d=2,3,4$ and 5 ($d$ is the spacetime dimension), which has uniform validity irrespectively of any specific values assumed for other parameters. Utilizing this series, precision evaluation of the renormalized functional determinant is possible with a relatively small number of low partial wave contributions determined separately. We illustrate the power of this scheme in numerically exact evaluation of the prefactor (expressed as a functional determinant) in the case of the false vacuum decay of 4D scalar field theory.

28 pages, 2 figures

References in corpus (12)

• Heisenberg-Euler Effective Lagrangians : Basics and Extensions
• Functional determinants by contour integration methods
• Beyond the thin-wall approximation : precise numerical computation of prefactors in false vacuum decay
• Functional determinants for radial operators
• One-loop corrections to the metastable vacuum decay
• Precise Quark Mass Dependence of Instanton Determinant
• Calculation of QCD Instanton Determinant with Arbitrary Mass
• Massive field contributions to the QCD vacuum tunneling amplitude
• Instanton Determinant with Arbitrary Quark Mass: WKB Phase-shift Method and Derivative Expansion
• Covariant derivative expansion of the heat kernel
• Renormalized Effective Actions in Radially Symmetric Backgrounds I: Partial Wave Cutoff Method
• Renormalized Effective Actions in Radially Symmetric Backgrounds: Exact Calculations Versus Approximation Methods

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• Full mass range analysis of the QED effective action for an O(2)xO(3) symmetric field
• Analytic Form of the QCD Instanton Determinant for Small Quark Mass
• Simplified Vacuum Energy Expressions for Radial Backgrounds and Domain Walls
• 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