On the Problem of Radiation Friction Beyond Four and Six Dimensions

Abstract

We count the number of independent structures which can arise in expressions for radiation friction force in different even space-time dimensions and demonstrate that their number is too big at d ≥ 8 to allow determination of this force from the transversality condition alone, as was done by B.Kosyakov in 6d. This implies that in general one can not bypass a tedious calculation involving explicit regularization and evaluation of emerging counterterms. However, simple Kosyakov's method works nicely in any dimension for the special case of circular motion with constant angular velocity.

Self-interaction and regularization of classical electrodynamics in higher dimensions

“…In this way, one can predict the formula for radiation friction for D = 4, 6. This approach is discussed in [7,8], while for D ≥ 8 it fails, and one has to use another technique.…”

“…A receipt for obtaining the equations of motion based on rather general principles relating radiation and radiation friction is described in [7] in six-dimensional space-time. Unfortunately, this technique fails already in eight dimensions, see [8]. Therefore, in order to come to higher dimensions, we apply here the method of expansion to series described in [6].…”

Geometric Hamiltonian formalism for reparameterization-invariant theories with higher derivatives

“…This (term in the) Lagrangian is encountered in radiation theory (see [14,15,16]). The Lagrangian containing this term, namely the Lagrangian for the relativistic particle with curvature, is also studied in, for example, [17].…”

Hamiltonian formalisms and symmetries of the Pais–Uhlenbeck oscillator

“…Originally, these theories were proposed as a method for dealing with ultraviolet divergences [2]; this idea appeared to be quite successful in the case of gravity: the Einstein action supplied by the terms containing higher powers of curvature leads to a renormalizable theory [3]. Other examples of higher derivatives theories include the theory of the radiation reaction [4,5], the field theory on noncommutative spacetime [6,7], anyons [8,9] or string theories with the extrinsic curvature [10].…”