On the Problem of Radiation Friction Beyond 4 and 6 Dimensions

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.