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Dirac-Hestenes Lagrangian

Authors:	Stefano De Leo Zbigniew Oziewicz Waldyr A Rodrigues Jayme Vaz

Abstract:	We formulate the variational principle of theDirac equation within the noncommutative even space-timesubalgebra, the Clifford $\mathbb{R}$ -algebra ${Cl_{_{1,3} }^ + }$ . A fundamental ingredient in ourmultivectorial algebraic formulation is a $\mathbb{D}$ -complex geometry, $\mathbb{D} \equiv {span}_\mathbb{D} \left\{ {1,{\gamma }_{{21}} } \right\},{\gamma }_{{21}} \in Cl_{_{1,3} }^ +$ . We derive the Lagrangian for theDirac-Hestenes equation and show that it must be mapped on $\mathbb{D} \otimes \mathcal{F}$ , where denotes an $\mathbb{R}$ -algebra of functions.

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