Functional determinants for radial operators

2006/07/11 by Gerald V. Dunne, Klaus Kirsten · 1 citation
Mathematics · Physics and Astronomy · #Cold Atom Physics and Bose-Einstein Condensates #Quantum Mechanics and Applications #Quantum, superfluid, helium dynamics #hep-ph #hep-th #math-ph #math.MP

paper · pdf · doi:10.1088/0305-4470/39/38/017

published as J.Phys.A39:11915-11928,2006 · 21 pages, uses axodraw.sty

arxiv created 2006/07/11 · openalex publication_date 2006/09/05 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/02

Abstract

We derive simple new expressions, in various dimensions, for the functional determinant of a radially separable partial differential operator, thereby generalizing the one-dimensional result of Gel'fand and Yaglom to higher dimensions. We use the zeta function formalism, and the results agree with what one would obtain using the angular momentum cutoff method based on radial WKB. The final expression is numerically equal to an alternative expression derived in a Feynman diagrammatic approach, but is considerably simpler.

Citations

• Fate of the false vacuum: Semiclassical theory
• Fate of the false vacuum. II. First quantum corrections
• On determinants of Laplacians on Riemann surfaces
• On the metastability of the Standard Model vacuum
• Functional determinants for general Sturm–Liouville problems

Cited by

• Renormalized effective actions in radially symmetric backgrounds: Exact calculations versus approximation methods