Calculation of the self force using the extended-object approach

Abstract

We present the extended-object approach for the explanation and calculation of the self-force phenomenon (often called “radiation-reaction force”). In this approach, one considers a charged extended object of a finite size ε that accelerates in a nontrivial manner, and calculates the total force exerted on it by the electromagnetic field (whose source is the charged object itself). We show that at the limit ε→0 this overall electromagnetic field yields a universal result, independent of the object’s shape, which agrees with the standard expression for the self force acting on a point-like charge. Previous implementation of this approach ended up with expressions for the total electromagnetic force that include O(1/ε) terms which do not have the form required by mass-renormalization. (In the special case of a spherical charge distribution, this ∝1/ε term was found to be 4/3 times larger than the desired quantity.) We show here that this problem was originated from a too naive definition of the notion of “total electromagnetic force” used in previous analyses. We then derive the correct notion of total electromagnetic force. This completely cures the problematic O(1/ε) term, for any object’s shape, and yields the correct self force at the limit ε→0. In particular, for a spherical charge distribution, the above “4/3 problem” is resolved.