Using the Clifford bundle formalism we show that Frenet equations of classical differential geometry or its spinor version are the appropriate equations of motion for a classical spinning particle. We show that particular values of the curvatures appearing in Darboux bivector of the spinor form of Frenet equations produce a "classical" Dirac-Hestenes equation. Using the concept of multivector Lagrangians and Hamiltonians we provide a Lagrangian and Hamiltonian approach for our theory which then makes immediately contact with Berezin-Marinov model, the Barut-Zanghi model, and the supercalculus (which acquires an obvious geometrical meaning in terms of geometrical objects living in ordinary spacetime) and suggests calling our theory the dynamics of the superparticle.
@article{bwmeta1.element.bwnjournal-article-bcpv37i1p295bwm,
author = {Rodrigues, Waldyr and Vaz, Jayme and Pavsic, Matej},
title = {The Clifford bundle and the dynamics of the superparticle},
journal = {Banach Center Publications},
volume = {37},
year = {1996},
pages = {295-314},
zbl = {1010.81507},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-bcpv37i1p295bwm}
}
Rodrigues, Waldyr; Vaz, Jayme; Pavsic, Matej. The Clifford bundle and the dynamics of the superparticle. Banach Center Publications, Tome 37 (1996) pp. 295-314. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-bcpv37i1p295bwm/
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