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Notes on the Feynman path integral for the Dirac equation

  • Wataru Ichinose
Article
  • 56 Downloads

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.

Keywords

The Feynman path integral Dirac equation Unitarity Causality 

Mathematics Subject Classification

81Q30 35Q40 

Notes

Acknowledgements

This work is partially supported by JSPS KAKENHI Grant Number 2640016.

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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Department of MathematicsShinshu UniversityMatsumotoJapan

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