On the Problem of Radiation Friction Beyond 4 and 6 Dimensions

TL;DR

This paper investigates the complexity of radiation friction forces in higher even-dimensional space-times, revealing limitations of existing methods and identifying cases where simplified approaches remain effective.

Contribution

It counts independent structures in radiation friction expressions across dimensions and shows the limitations of transversality conditions in dimensions eight and above.

Findings

Number of structures grows too large at d≥8

Transversality condition alone is insufficient in high dimensions

Kosyakov's method works for circular motion in all 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\geq 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.