Scalar heat kernel with boundary in the worldline formalism

Understand

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.