The Dirac-Hestenes Lagrangian

Abstract

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

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

References in corpus (1)

• Complex Geometry and Dirac Equation

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