An analog of the Feynman-Kac formula for Dirac's electron in electromagnetic field and the correspondence principle

TL;DR

This paper establishes a Feynman-Kac type relation for Dirac's electron in an electromagnetic field, linking quantum solutions to classical relativistic mechanics through functional analysis.

Contribution

It introduces an analog of the Feynman-Kac formula for Dirac's electron in electromagnetic fields, bridging quantum and classical descriptions.

Findings

Derived a relation between fundamental solutions of Dirac's equations

Connected quantum solutions to classical relativistic mechanics

Provided a functional framework for electron behavior in fields

Abstract

The article describes a relation between the fundamental solutions of Dirac's equations for free electron and electron in given electromagnetic field viewed as functionals on bump functions. We explain how classical relativistic mechanics of a charged particle in given electromagnetic field arises from quantum mechanics of Dirac's electron in that field.