Notes on the Feynman path integral for the Dirac equation

Abstract

This paper is a continuation of the author's preceding one. In the preceding paper the author has rigorously constructed the Feynman path integral for the Dirac equation in the form of the sum-over-histories, satisfying the superposition principle, over all paths of one electron in space-time that goes in any direction at any speed, forward and backward in time with a finite number of turns. In the present paper, first we will generalize the results in the preceding paper and secondly prove in a direct way that our Feynman path integral satisfies the unitarity principle and the causality one.