Vector fields on a disk with mixed boundary conditions
- 1 June 1995
- journal article
- Published by AIP Publishing in Journal of Mathematical Physics
- Vol. 36 (6) , 3174-3182
- https://doi.org/10.1063/1.531021
Abstract
We study vector fields on a disk satisfying two types of mixed boundary conditions. These boundary conditions are selected by BRST-invariance in electrodynamics. They also appear in the de Rham complex. The manifest construction of the harmonic expansion is presented. The eigenfunctions of the vector Laplace operator are expressed in terms of fields satisfying pure Dirichlet or Robin boundary conditions. For the case of four-dimensional disk several first coefficients of the heat kernel expansion are computed. An error in the analitical expression by Branson and Gilkey is corrected.Comment: 15 pp, Latex, SPbU-IP-94-Keywords
All Related Versions
This publication has 23 references indexed in Scilit:
- The functional integral for fields in a cavityJournal of Mathematical Physics, 1993
- Quantum cosmology with antisymmetric tensor fieldsPhysics Letters B, 1990
- The Asymptotics of The Laplacian on a Manifold with BoundaryCommunications in Partial Differential Equations, 1990
- The quantum geometry of random surfaces and spinning membranesClassical and Quantum Gravity, 1989
- Conformal invariance and the regularised one-loop effective actionJournal of Physics A: General Physics, 1988
- Quantum cosmology with electromagnetismPhysical Review D, 1988
- Semiclassical path measure and factor ordering in quantum cosmologyAnnals of Physics, 1988
- Semiclassical wave function of the Universe at small three-geometriesPhysical Review D, 1985
- Eigenvalues and degeneracies for n-dimensional tensor spherical harmonicsJournal of Mathematical Physics, 1984
- Ground-state wave function of linearized gravityPhysical Review D, 1984