Multiple reflection expansion and heat kernel coefficients

Abstract

We propose the multiple reflection expansion as a tool for the calculation of heat kernel coefficients. As an example, we give the coefficients for a sphere as a finite sum over reflections, obtaining as a byproduct a relation between the coefficients for Dirichlet and Neumann boundary conditions. Further, we calculate the heat kernel coefficients for the most general matching conditions on the surface of a sphere, including those cases corresponding to the presence of delta and delta prime background potentials. In the latter case, the multiple reflection expansion is shown to be non-convergent.

21 pages, corrected for some misprints

References in corpus (1)

• Heat trace asymptotics with transmittal boundary conditions and quantum brane-world scenario

Cited by in corpus (11)

• Heat kernel expansion: user's manual
• High temperature asymptotics of thermodynamic functions of electromagnetic field subjected to boundary conditions on a sphere and cylinder
• Potential theory, path integrals and the Laplacian of the indicator
• Boundary dynamics and multiple reflection expansion for Robin boundary conditions
• Integral Equations for Heat Kernel in Compound Media
• Local Neumann semitransparent layers: resummation, pair production and duality
• Divergences in the vacuum energy for frequency-dependent interactions
• Resummed heat-kernel for surface contributions: Dirichlet semitransparent boundary conditions
• Heat trace asymptotics defined by transfer boundary conditions
• Effects of Curvature-Scalar Coupling on Vacuum Energy in Flat (3+1)-Dimensional Space-Time
• Vacuum energy of scalar fields on spherical shells with general matching conditions