QFT over the finite line. Heat kernel coefficients, spectral zeta functions and selfadjoint extensions

DOI10.1007/s11005-015-0750-5zbMath1325.81114arXiv1402.7176OpenAlexW3103144033MaRDI QIDQ490741

Michael Bordag, Klaus Kirsten, José María Muñoz-Castañeda

Publication date: 28 August 2015

Published in: Letters in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1402.7176

zbMATH Keywords

quantum theoryscattering theoryCasimir effectboundary value problems for second-order elliptic equationsgeneral theory of linear operatorsparameter dependent boundary value problemsquantum field theory on curved space backgroundssymmetric and selfadjoint operatorszeta and \(L\)-functions: analytic theory

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Spectrum, resolvent (47A10) Linear symmetric and selfadjoint operators (unbounded) (47B25) Quantum field theory on curved space or space-time backgrounds (81T20) General quantum mechanics and problems of quantization (81S99) Selberg zeta functions and regularized determinants; applications to spectral theory, Dirichlet series, Eisenstein series, etc. (explicit formulas) (11M36) Quantum scattering theory (81U99) Parameter dependent boundary value problems for ordinary differential equations (34B08) Casimir effect in quantum field theory (81T55)

Related Items (6)

Effective computation of traces, determinants, and \(\zeta\)-functions for Sturm-Liouville operators ⋮ Boundaries without boundaries ⋮ Casimir pistons with generalized boundary conditions: a step forward ⋮ Spectral \(\zeta\)-functions and \(\zeta\)-regularized functional determinants for regular Sturm-Liouville operators ⋮ Revisiting the Casimir energy with general boundary conditions and applications in 1D crystals ⋮ Near-Dirichlet quantum dynamics for a \(p^3\)-corrected particle on an interval

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Double-delta potentials: One dimensional scattering
• Heat-kernels and functional determinants on the generalized cone
• Spectral theory for perturbed Krein Laplacians in nonsmooth domains
• Zeta function regularization of path integrals in curved spacetime
• Heat kernel expansion: user's manual
• Functional determinants by contour integration methods.
• Zeta function determinant of the Laplace operator on the \(D\)-dimensional ball
• Attractive and repulsive Casimir vacuum energy with general boundary conditions
• R-torsion and the Laplacian on Riemannian manifolds
• Quantum vacuum interaction between two sine-Gordon kinks
• Zeta function on surfaces of revolution
• GLOBAL THEORY OF QUANTUM BOUNDARY CONDITIONS AND TOPOLOGY CHANGE
• Functional determinants for general Sturm–Liouville problems
• Robin conditions on the Euclidean ball
• A Survey on the Krein–von Neumann Extension, the Corresponding Abstract Buckling Problem, and Weyl-type Spectral Asymptotics for Perturbed Krein Laplacians in Nonsmooth Domains
• Heat kernel coefficients of the Laplace operator on the D-dimensional ball
• Vacuum energy and renormalization on the edge
• Casimir effect and global theory of boundary conditions
• Advances in the Casimir Effect
• Vacuum boundary effects
• New developments in the Casimir effect

This page was built for publication: QFT over the finite line. Heat kernel coefficients, spectral zeta functions and selfadjoint extensions