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

Streszczenie

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.

Autorzy

  • Waldyr Rodrigues
  • Jayme Vaz
  • Matej Pavsic

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