On the Dirac Equation in 3 + 1 Dimensions
Abstract
The derivation of the kernel for the Feynman chessboard model in 1 + 1 dimensions is sketched in such a way that a formal extension to 3 + 1 dimensions is readily obtained. This extension is then examined so as to clarify the nature of the paths in three-dimensional space. We also consider how stochastic processes in 3 + 1 dimensions lead essentially to a "diagonalized" version of the (3 + 1) dimensional Dirac equation. This confirms the "transfer matrix" view that the Feynman paths are essentially one-dimensional.
- Publication:
-
Annals of Physics
- Pub Date:
- March 1993
- DOI:
- 10.1006/aphy.1993.1022
- Bibcode:
- 1993AnPhy.222..244O