Heat kernel asymptotics for mixed boundary conditions

Abstract

An asymptotic expansion for the heat kernel GDelta (x,x'; tau ) corresponding to a second order elliptic differential operator Delta acting on fields over manifolds with boundary is given. This expansion takes the form of an extended DeWitt ansatz satisfying mixed Dirichlet and Neumann boundary conditions. The functional trace, calculated directly using this expansion, agrees with more indirect derivations. The results are also represented as a distribution for general x,x' which, when integrated over the manifold, agree with other calculations carried out in the pure Dirichlet limit.