19th Capra Meeting on Radiation Reaction in General Relativity

Speaker : A. Popov

Title : Renormalization for the self-potential of a charge in static space-times

Abstract : The self-force is a force originating from the coupling between the charge of a particle and the field that this charge induces. The field induced by the point particle diverges at the particle’s location, and therefore a regularization method is required to calculate the correct (and finite) self-force from this diverging field. For this problem, formal expressions for the self-force have been derived for various types of fields. Some of them are reviewed in [Hikida:2005, Barack:2009]. Note also the zeta function method [Lousto:2000] and the "massive field approach" for the calculation of the self-force [Rosenthal:2004]. In the ultrastatic space-times the renormalization of the field of static charge can be realized by the subtraction of the first terms from DeWitt-Schwinger asymptotic expansion of a three-dimensional Euclidean Green’s function [Khus:2007, Krasnikov:2008, Bezerra:2009, Popov:2010]. In this work a similar approach expands to the case of static space-times. In the framework of the suggested procedure one subtracts some terms of expansion of the corresponding Green’s function of a massive scalar field with arbitrary coupling to the scalar curvature from the divergent expression obtained. The quantities of terms to be subtracted are defined by a simple rule — they no longer vanish as the field’s mass goes to infinity. Such an approach is similar to renormalization introduced in the context of the quantum field theory in curved space-time [DeWitt:1965, Christensen:1978]. The Bunch and Parker method [Bunch:1979] is used for expansion of the corresponding Green’s function of a scalar field. We also implement this method to calculate analytically the scalar self-force on a particle, which is held static in the background of some wormhole spacetimes.

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