Functional Determinants in Quantum Field Theory

Abstract

Functional determinants of differential operators play a prominent role in theoretical and mathematical physics, and in particular in quantum field theory. They are, however, difficult to compute in non-trivial cases. For one dimensional problems, a classical result of Gel'fand and Yaglom dramatically simplifies the problem so that the functional determinant can be computed without computing the spectrum of eigenvalues. Here I report recent progress in extending this approach to higher dimensions (i.e., functional determinants of partial differential operators), with applications in quantum field theory.

Plenary talk at QTS5 (Quantum Theory and Symmetries); 16 pp, 2 figs

References in corpus (27)

• Heat kernel expansion: user's manual
• On the metastability of the Standard Model vacuum
• Heisenberg-Euler Effective Lagrangians : Basics and Extensions
• From relativistic quantum fields to condensed matter and back again: Updating the Gross-Neveu phase diagram
• Functional determinants by contour integration methods
• Quantum weights of dyons and of instantons with non-trivial holonomy
• Functional determinants for general Sturm-Liouville problems
• Oscillating bounce solutions and vacuum tunneling in de Sitter spacetime
• Beyond the thin-wall approximation : precise numerical computation of prefactors in false vacuum decay
• Quantum Fluctuations around the Electroweak Sphaleron
• Quantum diffusion of magnetic fields in a numerical worldline approach
• Loops and loop clouds - a numerical approach to the worldline formalism in QED -
• Functional determinants for radial operators
• Regularisation of functional determinants using boundary perturbations
• One-loop corrections to the metastable vacuum decay
• Quantum fluctuations of the electroweak sphaleron: Erratum and Addendum
• Precise Quark Mass Dependence of Instanton Determinant
• Calculation of QCD Instanton Determinant with Arbitrary Mass
• Fluctuations about Cosmological Instantons
• QED in inhomogeneous magnetic fields
• The Barnes zeta-function, sphere determinants and Glaisher- Kinkelin-Bendersky constants
• Instanton Determinant with Arbitrary Quark Mass: WKB Phase-shift Method and Derivative Expansion
• Tunnel Determinants
• One-loop fermionic corrections to the instanton transition in two dimensional chiral Higgs model
• Metastability of (d+n)-dimensional elastic manifolds
• Fermion determinant for general background gauge fields
• Functional determinants on spheres and sectors

Cited by in corpus (57)

• Stability, Higgs Boson Mass and New Physics
• The lifetime of the electroweak vacuum and sensitivity to Planck scale physics
• No Rescue for the No Boundary Proposal
• Effective field theory approach to thermal bubble nucleation
• Generalized cusp in AdS_4 x CP^3 and more one-loop results from semiclassical strings
• Precision calculation of 1/4-BPS Wilson loops in AdS${}_5\times S^5$
• Perturbative computation of string one-loop corrections to Wilson loop minimal surfaces in $Ad{S}_5\times S^5$
• Green's function method for handling radiative effects on false vacuum decay
• Correlation Function of Circular Wilson Loops at Strong Coupling
• Formulating the Kramers problem in field theory
• Pohlmeyer-reduced form of string theory in AdS_5 x S^5: semiclassical expansion
• Kinks of open superstring field theory
• $\mathcal{P}\mathcal{T}$-symmetric $-g{\phi }^4$ theory
• Critical Points at Infinity, Non-Gaussian Saddles, and Bions
• Partition function on spheres: how (not) to use zeta function regularization
• Phase solitons and subgap excitations in two-band superconductors
• Symmetries and zero modes in sample path large deviations
• Chiral soliton lattice at next-to-leading order
• Exact one-loop false vacuum decay rate
• Gel'fand-Yaglom type equations for calculating fluctuations around Instantons in stochastic systems
• Analytic thin wall false vacuum decay rate
• False vacuum decay rates, more precisely
• $T\bar{T}+{\Lambda }_2$ from a 2d gravity path integral
• Conditional probabilities in multiplicative noise processes
• Two-loop corrections to false vacuum decay in scalar field theory
• Computing black hole partition functions from quasinormal modes
• False vacuum decay of excited states in finite-time instanton calculus
• Simulating Quantum Mechanics with a $\theta$-term and an 't Hooft Anomaly on a Synthetic Dimension
• State dependent diffusion in a bistable potential: conditional probabilities and escape rates
• Radiative corrections to false vacuum decay in quantum mechanics
• A Note on a Differential Galois Approach to Path Integrals
• Simple way to calculate UV-finite one-loop quantum energy in Randall-Sundrum model
• Fluctuation corrections to Lifshitz tails in disordered systems
• Wilson Loops and Spherical Branes
• Instanton gas approach to the Hubbard model
• Quantum corrections to minimal surfaces with mixed three-form flux
• Thermal Effective Lagrangian of Static Gravitational Fields
• Boundary choices and one-loop complex gravitational path integral
• Introductory Lectures on Resurgence: CERN Summer School 2024
• Index theorems for graph-parametrized optimal control problems
• Green's Matrix for a Second Order Self-Adjoint Matrix Differential Operator
• Mesoscopic supercurrent fluctuations in diffusive magnetic Josephson junctions
• On the quantum equivalence of an antisymmetric tensor field with spontaneous Lorentz violation
• Spectral determinants for twist field correlators
• Scaling Dimensions in AdS/QCD and the Gluon Field Strength Propagator
• Adiabatic regularization of functional determinants in cosmology and radiative corrections during inflation
• Noise equals control
• A note on a gauge-gravity relation and functional determinants
• Fermions and Kaluza-Klein vacuum decay: a toy model
• Vortex Formation in Two-Dimensional Bose Gas
• Relational de Sitter State Counting with an SU(3) Clock
• Simplified Vacuum Energy Expressions for Radial Backgrounds and Domain Walls
• The influence of the Casimir effect on the binding potential for 3D wetting
• On equivalent methods for functional determinants
• Path-integral approach to Casimir effect with infinitely thin plates
• New asymptotic techniques for the partial wave cut-off method for calculating the QED one loop effective action
• Functional Determinants for Constrained Path Integrals in Minisuperspace Jackiw-Teitelboim Gravity