Dirac particle with memory: Proper time non-locality

Abstract

A generalization of the standard model of Dirac particle in external electromagnetic field is proposed. In the generalization we take into account interactions of this particle with environment, which is described by the memory function. This function takes into account that the behavior of the particle at proper time can depend not only at the present time, but also on the history of changes on finite time interval. In this case the Dirac particle can be considered an open quantum system with non-Markovian dynamics. The violation of the semigroup property of dynamic maps is a characteristic property of dynamics with memory. We use the Fock-Schwinger proper time method and derivatives of non-integer orders with respect to proper time. The fractional differential equation, which describes the Dirac particle with memory, and the expression of its exact solution are suggested. The asymptotic behavior of the proposed solutions is described.