The Clifford bundle and the dynamics of the superparticle

Tom 37 / 1996

Waldyr Rodrigues, Jayme Vaz, Matej Pavsic Banach Center Publications 37 (1996), 295-314 DOI: 10.4064/-37-1-295-314


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.


  • Waldyr Rodrigues
  • Jayme Vaz
  • Matej Pavsic

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