The Dirac-Hestenes Lagrangian

Details The Dirac-Hestenes Lagrangian The Dirac-Hestenes Lagrangian

1999-06-03

arxiv.org/abs/hep-ph/9906243v1

Int.J.Theor.Phys. 38 (1999) 2349-2369

Physics

High Energy Physics

High Energy Physics - Phenomenology

14 pages, RevTex. To appear in Int. J. Theor. Phys

Scientific paper

We discuss the variational principle within Quantum Mechanics in terms of the noncommutative even Space Time sub-Algebra, the Clifford $\Ra$-algebra $Cl_{1,3}^+$. A fundamental ingredient, in our multivectorial algebraic formulation, is the adoption of a $\D $-complex geometry, $\D \equiv span_{\RR} \{1,\gamma_{21} \}$, $\gamma_{21} \in Cl_{1,3}^+$. We derive the Lagrangian for the Dirac-Hestenes equation and show that such Lagrangian must be mapped on $\D \otimes {\cal F}$, where $\cal F$ denotes an $\Ra$-algebra of functions.

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