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The Clifford Algebra Approach to Quantum Mechanics B: The Dirac Particle and its relation to the Bohm Approach | | B.J.Hiley
; R.E.Callaghan
; | | Date: |
17 Nov 2010 | | Abstract: | In this paper we present for the first time a complete description of the
Bohm model of the Dirac particle. This result demonstrates again that the
common perception that it is not possible to construct a fully relativistic
version of the Bohm approach is incorrect. We obtain the fully relativistic
version by using an approach based on Clifford algebras outlined in two earlier
papers by Hiley and by Hiley and Callaghan. The relativistic model is different
from the one originally proposed by Bohm and Hiley and by Doran and Lasenby. We
obtain exact expressions for the Bohm energy-momentum density, a relativistic
quantum Hamilton-Jacobi for the conservation of energy which includes an
expression for the quantum potential and a relativistic time development
equation for the spin vectors of the particle. We then show that these reduce
to the corresponding non-relativistic expressions for the Pauli particle which
have already been derived by Bohm, Schiller and Tiomno and in more general form
by Hiley and Callaghan. In contrast to the original presentations, there is no
need to appeal to classical mechanics at any stage of the development of the
formalism. All the results for the Dirac, Pauli and Schroedinger cases are
shown to emerge respectively from the hierarchy of Clifford algebras
C(13),C(30), C(01) taken over the reals as Hestenes has already argued. Thus
quantum mechanics is emerging from one mathematical structure with no need to
appeal to an external Hilbert space with wave functions. | | Source: | arXiv, 1011.4033 | | Services: | Forum | Review | PDF | Favorites | |
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