Discrete versions of some Dirac type equations and plane wave solutions
Volodymyr Sushch
TL;DR
This paper develops discrete analogues of plane wave solutions for Dirac-type equations within spacetime algebra, exploring conditions for these solutions to satisfy discrete Hestenes equations.
Contribution
It introduces a discrete framework for Dirac equations and analyzes conditions for plane wave solutions to meet discrete Hestenes equations.
Findings
Discrete plane wave solutions are constructed.
Conditions for solutions to satisfy discrete Hestenes equations are identified.
The framework bridges continuous and discrete Dirac equations.
Abstract
A discrete version of the plane wave solution to some discrete Dirac type equations in the spacetime algebra is established. The conditions under which a discrete analogue of the plane wave solution satisfies the discrete Hestenes equation are briefly discussed.
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