Multiple reflection expansion and heat kernel coefficients - art. no. 045017

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 relati on between the coefficients for Dirichlet and Neumann boundary conditions. Further, we calculate the heat kernel coefficients for the most general mat ching conditions on the surface of a sphere, including those cases correspo nding to the presence of delta and delta prime background potentials. In th e latter case, the multiple reflection expansion is shown to be nonconverge nt.