Notes on the Feynman path integral for the Dirac equation
- 80 Downloads
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.
KeywordsThe Feynman path integral Dirac equation Unitarity Causality
Mathematics Subject Classification81Q30 35Q40
This work is partially supported by JSPS KAKENHI Grant Number 2640016.
- 2.Dyson, F.: Comment on the topic “Beyond the black hole”. In: Some Strangeness in the Proportion: A Centennial Symposium to Celebrate the Achievements of Albert Einstein, pp. 376–380. Addison-Wesely, Reading (1980)Google Scholar
- 11.John, F.: Partial Differential Equations. 4th edn. Springer, New York (1982)Google Scholar