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arXiv · hep-ph/9906243

The Dirac-Hestenes Lagrangian

S. De Leo·Z. Oziewicz·J. Vaz·WA. Rodrigues
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Abstract

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, $\D \equiv span_{\RR} \{1,γ_{21} \}$, $γ_{21} \in Cl_{1,3}^+$. 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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S. De Leo, Z. Oziewicz, J. Vaz, WA. Rodrigues. 1999-06-03. The Dirac-Hestenes Lagrangian. https://doi.org/10.1023/a%3A1026627819148

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