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Journal Article

Scalar heat kernel with boundary in the worldline formalism


Bastianelli,  Fiorenzo
Quantum Gravity & Unified Theories, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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Bastianelli, F., Corradini, O., Pisani, P. A. G., & Schubert, C. (2008). Scalar heat kernel with boundary in the worldline formalism. Journal of High Energy Physics, 2008(10): 095. doi:10.1088/1126-6708/2008/10/095.

Cite as: http://hdl.handle.net/11858/00-001M-0000-0013-135B-8
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 Bbb R+ × Bbb RD−1, based on an extension of the associated worldline path integral to the full Bbb RD 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, a4 and a9/2.