The Clifford bundle and the dynamics of the superparticle

Waldyr Rodrigues; Jayme Vaz; Matej Pavsic

Banach Center Publications (1996)

  • Volume: 37, Issue: 1, page 295-314
  • ISSN: 0137-6934

Abstract

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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.

How to cite

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Rodrigues, Waldyr, Vaz, Jayme, and Pavsic, Matej. "The Clifford bundle and the dynamics of the superparticle." Banach Center Publications 37.1 (1996): 295-314. <http://eudml.org/doc/208606>.

@article{Rodrigues1996,
abstract = {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.},
author = {Rodrigues, Waldyr, Vaz, Jayme, Pavsic, Matej},
journal = {Banach Center Publications},
language = {eng},
number = {1},
pages = {295-314},
title = {The Clifford bundle and the dynamics of the superparticle},
url = {http://eudml.org/doc/208606},
volume = {37},
year = {1996},
}

TY - JOUR
AU - Rodrigues, Waldyr
AU - Vaz, Jayme
AU - Pavsic, Matej
TI - The Clifford bundle and the dynamics of the superparticle
JO - Banach Center Publications
PY - 1996
VL - 37
IS - 1
SP - 295
EP - 314
AB - 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.
LA - eng
UR - http://eudml.org/doc/208606
ER -

References

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