Heat-kernel coefficients of the Laplace operator on the 3-dimensional ball

Abstract

We consider the heat-kernel expansion of the massive Laplace operator on the three dimensional ball with Dirichlet boundary conditions. Using this example, we illustrate a very effective scheme for the calculation of an (in principle) arbitrary number of heat-kernel coefficients for the case where the basis functions are known. New results for the coefficients $B_{\frac 5 2},...,B_5$ are presented.