Author： Mosna R.A. Miralles D. Vaz Jr. J.
Publisher： Springer Publishing Company
ISSN： 0020-7748
Source： International Journal of Theoretical Physics, Vol.41, Iss.9, 2002-09, pp. : 1651-1671
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Abstract
We generalize certain aspects of Hestenes's approach to Dirac theory to obtain multivector Dirac equations associated to a large class of representations of the gamma matrices. This is done by replacing the usual even/odd decomposition of the space-time algebra with more general {Bbb Z}_2-gradings. Some examples are given and the chiral case, which is not addressed by the usual approach, is considered in detail. A Lagrangian formulation is briefly discussed. A relationship between this work and certain quaternionic models of the (usual) quantum mechanics is obtained. Finally, we discuss under what conditions the Hestenes's form can be recovered and we suggest a geometrical interpretation for the corresponding situation.
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