Dirac-Hestenes Lagrangian

We formulate the variational principle of the Dirac equation within the non commutative even space-time subalgebra, the Clifford BE-algebra Cl-1,3(+). A fundamental ingredient in our multivectorial algebraic formulation is a D -complex geometry, D = span(D) (I, gamma(21)), gamma(21) is an element of C l-1,3(+). We derive the Lagrangian for the Dirac-Hestenes equation and show that it must be mapped on D x F, where F denotes an R-algebra of functions .