An analysis of the landau-lifshitz reaction term in classical electrodynamics

Since Dirac obtained the so named Lorentz-Dirac equation [LD] as the equation of motion for a charged point particle, it has focused many discussions about its validity. Indeed, the runaway solutions, the preaccelerations, the renormalization of the electron's mass and the violation of physical causality by the use of the advanced solutions of the Maxwell equations, are the main reasons for the long historical discussion about the LD equation. This unsatisfactory situation is evidenced by the continued appearance of new equations of motion in the literature. By using an approximation of first order of the LD equation, Landau and Lifshitz obtained an equation in the frame of classical electrodynamics, the Landau-Lifshitz equation [LL]. Spohn has claimed that the LL equation can be obtained with the same degree of accuracy than the LD equation. Rohrlich has noticed that LL equation is a second order differential equation which doesn't permit runaway solutions or preaccelerations. It is important to note that Ares de Parga have proposed a physical deduction of the LL equation which implies a change in the concept of the radiation rate of energy; that is: The regular LD reaction term is substituted by the LL reaction term. We analyze the different situations where the LL reaction term vanishes. In these cases, the LL equation of motion coincides with the Lorentz equation. We propose some physical interpretations in order to understand the absence of radiation rate of energy in such situations.