Quantum Theory of Near-Field Electrodynamics pp 111-128 | Cite as

# Radiation Reaction

## Abstract

In Sect. 2.3, we discussed the solutions to the Maxwell–Lorentz equations, and (2.22) and (2.23) express the microscopic electric and magnetic fields in terms of certain integrals involving the microscopic charge and current densities. If these densities are prescribed (specified) (2.22) and (2.23) represent the physically general solution to the Maxwell–Lorentz equations. In near-field electrodynamics the charge and current densities can seldom be considered as prescribed quantities, but must be related to the local electromagnetic field acting on the particles. Hence, (2.22) and (2.23) only determine the microscopic field in implicit form. In the case of a single point-particle, the Lienard–Wiechert equations ((2.60)–(2.62) and (2.66)–(2.68)) give the electromagnetic field in terms of the velocity and acceleration of the particle. The particle acceleration causes emission of radiation, described by the acceleration fields in (2.62) and (2.68), and a correct treatment of the particle motion must include the reaction of the radiation on this motion. In our treatment of the electromagnetic interaction between point dipoles in Chap. 6, the radiative reaction of the dipole fields was neglected. Incorporation of this effect leads to a change in the local field as we shall see.