Robin conditions on the Euclidean ball

Abstract

Techniques are presented for calculating directly the scalar functional determinant on the Euclidean d-ball. General formulae are given for Dirichlet and Robin boundary conditions. The method involves a large mass asymptotic limit which is carried out in detail for d=2 and d=4 incidentally producing some specific summations and identities. Extensive use is made of the Watson-Kober summation formula.

36p,JyTex, misprints corrected and a section on the massive case added

References in corpus (3)

• Heat-kernel coefficients of the Laplace operator on the D-dimensional ball
• Local Boundary Conditions for the Dirac Operator and One-Loop Quantum Cosmology
• Further functional determinants

Cited by in corpus (17)

• Heat kernel expansion: user's manual
• Spectral invariants for the Dirac equation on the d-Ball with various boundary conditions
• The $a_{3/2}$ heat kernel coefficient for oblique boundary conditions
• The Dirichlet-to-Robin Transform
• QFT over the finite line. Heat kernel coefficients, spectral zeta functions and selfadjoint extensions
• Chiral bag boundary conditions on the ball
• The Barnes zeta-function, sphere determinants and Glaisher- Kinkelin-Bendersky constants
• Discrete Symmetries of Functional Determinants
• Boundary conditions and the entropy bound
• Heat-kernel coefficients and functional determinants for higher-spin fields on the ball
• One-Loop Effective Action for Euclidean Maxwell Theory on Manifolds with Boundary
• Vacuum destabilization from Kaluza-Klein modes in an inflating brane
• The hybrid spectral problem and Robin boundary conditions
• Radiative Contributions to the Effective Action of Self-Interacting Scalar Field on a Manifold with Boundary
• Small Mass Expansion of Functional Determinants on the Generalized Cone
• Discrete Determinants and the Gel'fand-Yaglom formula
• Remark on the computation of mode sums