ALTERNATIVE EQUATIONS OF MOTION FOR THE RADIATING ELECTRON

We have previously written down a simple second-order equation for the radiating electron and pointed out that its solutions are well behaved. A key feature of this equation is the presence of a term involving the time derivative of the external field f(t). Here, we show that a completely equivalent, but less elegant, equation may be written down which contains no derivatives of f(t) but, instead, an infinite number of derivatives of the coordinate. However, it has the merit of displaying explicitly how our result differs from that of Abraham-Lorentz.