Abstract
This chapter shows very clearly that the Clifford and spin-Clifford bundle formalism (introduced in previous chapters) offers a very simple way to write the equation of motion of a massive spinning particle. Indeed this equation is immediately derived from Frenet equations for a moving frame. Moreover, with addition of very a reasonable hypothesis the deduced spinor equation for the spinning particle leads directly to a classical (nonlinear) Dirac-Hestenes equation. An additional hypothesis leads to a linear Dirac-Hestenes equation and suggests automatically a probability interpretation for the Dirac-Hestenes wave function. We also show how the Clifford and spin-Clifford bundle formalism permit the introduction of multiform valued Lagrangians and a simple interpretation of the so-called superparticle theory. Moreover, the Berezin differential and integral calculus is shown to be no more than the result of contractions in an appropriate Clifford algebra. Also, the nature of superfields is clearly disclosed.
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Notes
- 1.
Of course, the question of renormalization of the wave function ϕ is to be deal in the same way as in standard quantum mechanics.
- 2.
This simple heuristic argument has been generalized in order to obtain the wave equation for a spin 1∕2 particle in [9].
- 3.
Compare this with the original Berezin-Marinov model [1], where it is necessary to use a pentadimensional Grassmann algebra in order to obtain the Dirac equation after quantization.
- 4.
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Rodrigues, W.A., Capelas de Oliveira, E. (2016). Superparticles and Superfields. In: The Many Faces of Maxwell, Dirac and Einstein Equations. Lecture Notes in Physics, vol 922. Springer, Cham. https://doi.org/10.1007/978-3-319-27637-3_14
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DOI: https://doi.org/10.1007/978-3-319-27637-3_14
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