Radiation damping as an initial value problem

Abstract

Using a simple, exactly soluble model for the interaction of one particle and a scalar field Φ, we discuss the problem of radiation reaction in terms of the initial value solution. We show that if the Cauchy data of the field fall off at spatial infinity in such a way that the field has finite energy, the particle motion is damped for t → ∞. Further, we point out that no solutions with finite field energy exist for the boundary conditions Φ out = 0 and Φ in + Φ out = 0. For Φ in = 0, nontrivial solutions exist only if it is assumed that the system has been open in the past of some initial hypersurface.