Relativistic charged-particle interactions in a chaotic laser field

Interactions of charged particles in the presence of a chaotic laser field are considered for the case where the quadratic $A^2$ term in the Volkov solution must be retained. This is necessary whenever the kinematics are relativistic or the masses of the particles involved change during the interaction, such as in a decay, even though the kinematics might be nonrelativistic. Spin terms of the Volkov solution are also considered. The problem reduces to the solution of a stationary Gaussian stochastic process. This allows for an explicit evaluation if the two-time correlation function of the laser field is exponential with an arbitrary correlation time, i.e., for an Ornstein-Uhlenbeck process. The evaluation is performed by two alternative methods, one relying on path integrals and the other one on functional methods. Various limiting cases are discussed, notably that of an infinite correlation time. In the latter case, a cross section in a chaotic field is obtained from that in a coherent field by integrating the latter over the intensity with an exponential weight function. This prescription was already known to hold in the nonrelativistic case. As an application, we discuss high-intensity Compton scattering. A specialization of the present results yields an ensemble average, which is needed in the evaluation of a recent $g-2\mathrm{}$ experiment for the anomalous magnetic moment of the electron.