Stochastic theory of relativistic particles moving in a quantum field: Scalar Abraham-Lorentz-Dirac-Langevin equation, radiation reaction, and vacuum fluctuations

We apply the open systems concept and the influence functional formalism to establish a stochastic theory of relativistic moving spinless particles in a quantum scalar field. The stochastic regime resting between the quantum and semiclassical regimes captures the statistical mechanical attributes of the full theory. Applying the particle-centric world line quantization formulation to describe charged particles in a scalar quantum field environment, we derive a modified Abraham-Lorentz-Dirac (ALD) equation with time-dependent coefficients and show that it is the correct semiclassical limit for nonlinear particle-field systems without the need of making the dipole or nonrelativistic approximations. Our modified ALD equation is causal and free of runaway solutions. We show this technically, as a consequence of the nonequilibrium open system dynamics, and conceptually, invoking decoherence. Progressing to the stochastic regime, we derive a relativistic ALD-Langevin (ALDL) equation for nonlinearly coupled charges in a scalar quantum field. The ALD and ALDL equations clarify the relation of radiation reaction, dissipation and vacuum fluctuations. This self-consistent treatment serves as a new platform for investigations into problems related to relativistic moving charges.