Pseudoclassical description of relativistic particles interacting with electromagnetic fields and weakly interacting with matter fields
Department of Physics, Tomsk State University, 634050, Tomsk, Russia
2 P. N. Lebedev Physical Institute, 53 Leninskiy Prospect, 119991, Moscow, Russia
3 Institute of Physics, University of São Paulo, Rua do Matão, 1371, 05508-090, São Paulo, SP, Brazil
Accepted: 21 September 2021
Published online: 1 October 2021
Starting from an equation for causal propagator describing Dirac particles interacting with electromagnetic fields and weakly interacting with matter fields, we derive a path integral representation for the propagator. An effective gauge invariant action, which appears in the representation, is interpreted as a pseudoclassical action for the Dirac particles. Quantization of the action is nontrivial due to its gauge invariant nature as well as due to ordering problems that arise in course of a realization of commutation relations in a Hilbert space. The Dirac equation in the background under consideration appears as a quantum equation of motion in the constructed quantum mechanics, justifying, thus, the interpretation of the action. The path-integral representation allows one to calculate effectively the propagator and with its help emerging quantum currents. Studying these currents one may detect effects similar to the chiral magnetic effect. Pseudoclassical equations of motion in the nonrelativistic limit generalize nontrivially the Pauli quantum mechanics with external electromagnetic field.
© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2021