Quantum theory of extended particle dynamics in the presence of EM radiation-reaction

In this paper a trajectory-based relativistic quantum wave equation is established for extended charged spinless particles subject to the action of the electromagnetic (EM) radiation-reaction (RR) interaction. The quantization pertains the particle dynamics, in which both the external and self EM fields are treated classically. The new equation proposed here is referred to as the RR quantum wave equation. This is shown to be an evolution equation for a complex scalar quantum wave function and to be realized by a first-order PDE with respect to a quantum proper time s . The latter is uniquely prescribed by representing the RR quantum wave equation in terms of the corresponding quantum hydrodynamic equations and introducing a parametrization in terms of Lagrangian paths associated with the quantum fluid velocity. Besides the explicit proper time dependence, the theory developed here exhibits a number of additional notable features. First, the wave equation is variational and is consistent with the principle of manifest covariance. Second, it permits the definition of a strictly positive 4-scalar quantum probability density on the Minkowski space-time, in terms of which a flow-invariant probability measure is established. Third, the wave equation is non-local, due to the characteristic EM RR retarded interaction. Fourth, the RR wave equation recovers the Schrödinger equation in the non-relativistic limit and the customary Klein-Gordon wave equation when the EM RR is negligible or null. Finally, the consistency with the classical RR Hamilton-Jacobi equation is established in the semi-classical limit.