RADIATION REACTION IN ELECTRODYNAMICS AND THE ELIMINATION OF RUNAWAY SOLUTIONS

The familiar Abraham-Lorentz theory of radiation reaction in classical non-relativistic electrodynamics exhibits many problems such as "runaway solutions" and violation of causality. As shown by many authors, such problems can be alleviated by dropping the assumption of a point electron. We also drop this assumption by introducing a form-factor with a large cutoff frequency-OMEGA) but we present a new approach based on the use of the generalized quantum Langevin equation. For an electric dipole interaction, an exact treatment is possible and we obtain a new equation of motion which, in spite of being third order. does not lead to runaway solutions or solutions which violate causality (the sole proviso being that OMEGA cannot exceed an upper limit of 3Mc3/2e2 = 1.60 x 10(23) s-1). Furthermore, OMEGA appears in the third-derivative term but we show that, to a very good approximation, this term may be dropped so that we end up with a simple second-order equation which does not contain OMEGA and whose solutions are well-behaved.