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.

Scalar heat kernel with boundary in the worldline formalism / Bastianelli, Fiorenzo; Corradini, Olindo; Pisani, Pablo A. G; Schubert, Christian. - In: JOURNAL OF HIGH ENERGY PHYSICS. - ISSN 1029-8479. - 0810 (2008) 095:(2008), pp. 0-20. [10.1088/1126-6708/2008/10/095]

Scalar heat kernel with boundary in the worldline formalism

CORRADINI, Olindo;
2008

Abstract

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.
2008
0810 (2008) 095
0
20
Scalar heat kernel with boundary in the worldline formalism / Bastianelli, Fiorenzo; Corradini, Olindo; Pisani, Pablo A. G; Schubert, Christian. - In: JOURNAL OF HIGH ENERGY PHYSICS. - ISSN 1029-8479. - 0810 (2008) 095:(2008), pp. 0-20. [10.1088/1126-6708/2008/10/095]
Bastianelli, Fiorenzo; Corradini, Olindo; Pisani, Pablo A. G; Schubert, Christian
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11380/1074542
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