Stochastic Theory of Relativistic Particles Moving in a Quantum Field: II. Scalar Abraham-Lorentz-Dirac-Langevin Equation, Radiation Reaction and Vacuum Fluctuations

摘要

We apply the open systems concept and the influence functional formalismintroduced in Paper I to establish a stochastic theory of relativistic movingspinless particles in a quantum scalar field. The stochastic regime restingbetween the quantum and semi-classical captures the statistical mechanicalattributes of the full theory. Applying the particle-centric world-linequantization formulation to the quantum field theory of scalar QED we derive atime-dependent (scalar) Abraham-Lorentz-Dirac (ALD) equation and show that itis the correct semiclassical limit for nonlinear particle-field systems withoutthe need of making the dipole or non-relativistic approximations. Progressingto the stochastic regime, we derive multiparticle ALD-Langevin equations fornonlinearly coupled particle-field systems. With these equations we show how toaddress time-dependent dissipation/noise/renormalization in the semiclassicaland stochastic limits of QED. We clarify the the relation of radiationreaction, quantum dissipation and vacuum fluctuations and the role that initialconditions may play in producing non-Lorentz invariant noise. We emphasize thefundamental role of decoherence in reaching the semiclassical limit, which alsosuggests the correct way to think about the issues of runaway solutions andpreacceleration from the presence of third derivative terms in the ALDequation. We show that the semiclassical self-consistent solutions obtained inthis way are ``paradox'' and pathology free both technically and conceptually.This self-consistent treatment serves as a new platform for investigations intoproblems related to relativistic moving charges.