Complex Geometry and Dirac Equation

Details Complex Geometry and Dirac Equation Complex Geometry and Dirac Equation

1999-05-17

arxiv.org/abs/hep-th/9905124v1

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.

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