The Classical Limit of the Quantum Theory of Radiation Damping

The classical limit of the quantum theory of damping (without radiative corrections) has been studied for scattering procedures involving photons and neutral or charge-symmetric mesons [with $S(S)$, PS(PV), $V(V)$, and $V(T)$ coupling] interacting with nucleons. In the case of dipole coupling the nuclear spin 1/2 must be replaced by a classical intrinsic angular momentum, and classical rather than quantum mechanical averages over spin variables must be taken. The cross sections are then calculated taking classical limits at all stages rather than just in the summation over the final stages. Comparison is made with the corresponding results in the classical field and action-at-a-distance theories; the cross sections agree with those of the theory of action at a distance in all cases for which these results are available.