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On Poisson brackets and symplectic structures for the classical and quantum zitterbewegung

  • Part III. Invited Papers Dedicated To David Hestenes
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Abstract

The symplectic structures (brackets, Hamilton's equations, and Lagrange's equations) for the Dirac electron and its classical model have exactly the same form. We give explicitly the Poisson brackets in the dynamical variables (x μ,p μ,v μ,S μv). The only difference is in the normalization of the Dirac velocities γμγμ=4 which has significant consequences.

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References

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Author notes

  1. A. O. Barut

    Present address: Physics Department, University of Colorado, 80309, Boulder, Colorado

  2. N. Ünal

    Present address: Physics Department, Akdeniz University, Antalya, Turkey

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    1. A. O. Barut
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    2. N. Ünal
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    Dedicated to David Hestenes, whose work profoundly connects geometry (spacetime), algebra (Clifford), and physics (electron).

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    Barut, A.O., Ünal, N. On Poisson brackets and symplectic structures for the classical and quantum zitterbewegung. Found Phys 23, 1423–1429 (1993). https://doi.org/10.1007/BF01243939

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    • DOI: https://doi.org/10.1007/BF01243939

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