On equivalent methods for functional determinants
arXiv:2601.08686 · doi:10.1007/JHEP06(2026)073
Abstract
Computing functional determinants of differential operators is central to any field-theoretical calculation relying on a saddle-point expansion. A variety of approaches is available for the computation that avoid having to know the eigenspectrum of the operator, and in particular the Gel'fand-Yaglom theorem and the Green's function method. In this note, we show how both approaches can be constructed using a contour integral argument and conclude that these are completely equivalent for computing ratios of determinants of one-dimensional operators. Furthermore, we comment on the presence of vanishing as well as negative eigenvalues and show how the Green's function method provides a natural prescription for handling them.
arXiv comment17 pages, 3 figures
References in corpus (24)
- Higgs mass and vacuum stability in the Standard Model at NNLO
- Heat kernel expansion: user's manual
- On the metastability of the Standard Model vacuum
- Functional determinants by contour integration methods
- Scale Invariant Instantons and the Complete Lifetime of the Standard Model
- Functional determinants for general Sturm-Liouville problems
- Beyond the thin-wall approximation : precise numerical computation of prefactors in false vacuum decay
- Functional Determinants in Quantum Field Theory
- Quantum Fluctuations around the Electroweak Sphaleron
- One-Loop Corrections to Bubble Nucleation Rate at Finite Temperature
- Decay Rate of Electroweak Vacuum in the Standard Model and Beyond
- Functional determinants for radial operators
- Regularisation of functional determinants using boundary perturbations
- Quantum fluctuations of the electroweak sphaleron: Erratum and Addendum
- One-loop corrections to the metastable vacuum decay
- BubbleDet: A Python package to compute functional determinants for bubble nucleation
- Domain walls seeding the electroweak phase transition
- Green's function method for handling radiative effects on false vacuum decay
- Higher-Order Corrections to the Bubble-Nucleation Rate at Finite Temperature
- One-loop corrections to the instanton transition in the Abelian Higgs model: Gel'fand-Yaglom and Green's function methods
- Quantum Corrections to the Electroweak Sphaleron Transition
- Double-well instantons in finite volume
- QCD Axion Strings or Seeds?
- False vacuum decay beyond the quadratic approximation: summation of non-local self-energies