Scalar heat kernel with boundary in the worldline formalism

Bastianelli, Fiorenzo; Corradini, Olindo; Pisani, Pablo A. G.; Schubert, Christian

Scalar heat kernel with boundary in the worldline formalism

Authors

Bastianelli, Fiorenzo

Corradini, Olindo

Pisani, Pablo A. G.

Schubert, Christian

Description

The worldline formalism has in recent years emerged as a powerful tool for the computation of effective actions and heat kernels. However, implementing nontrivial boundary conditions in this formalism has turned out to be a difficult problem. Recently, such a generalization was developed for the case of a scalar field on the half-space R_+ x R^{D-1}, based on an extension of the associated worldline path integral to the full R^D using image charges. We present here an improved version of this formalism which allows us to write down non-recursive master formulas for the n-point contribution to the heat kernel trace of a scalar field on the half-space with Dirichlet or Neumann boundary conditions. These master formulas are suitable to computerization. We demonstrate the efficiency of the formalism by a calculation of two new heat-kernel coefficients for the half-space, a_4 and a_{9/2}.
1+21 pages; references added, published version