Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1999-05-17
Int.J.Theor.Phys. 37 (1998) 2479
Physics
High Energy Physics
High Energy Physics - Theory
11 pages, RevTex
Scientific paper
Complex geometry represents a fundamental ingredient in the formulation of the Dirac equation by the Clifford algebra. The choice of appropriate complex geometries is strictly related to the geometric interpretation of the complex imaginary unit $i=\sqrt{-1}$. We discuss {\em two} possibilities which appear in the multivector algebra approach: the $\sigma_{123}$ and $\sigma_{21}$ complex geometries. Our formalism permits to perform a set of rules which allows an immediate translation between the complex standard Dirac theory and its version within geometric algebra. The problem concerning a double geometric interpretation for the complex imaginary unit $i=\sqrt{-1}$ is also discussed.
Leo Stefano de
Rodrigues WA
Vaz Jayme
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