The Dirac–Hestenes Equation and its Relation with the Relativistic de Broglie–Bohm Theory

The Dirac–Hestenes Equation and its Relation with the Relativistic de Broglie–Bohm Theory In this paper we provide using the Clifford and spin-Clifford formalism and some few results of the extensor calculus a derivation of the conservation laws that follow directly from the Dirac–Hestenes equation (DHE) describing a Dirac–Hestenes spinor field (DHSF) in interaction with an external electromagnetic field without using the Lagrangian formalism. In particular, we show that the energy-momentum and total angular momentum extensors of a DHSF is not conserved in spacetime regions permitting the existence of a null electromagnetic field F but a non null electromagnetic potential $$A $$ A . These results have been used together with some others recently obtained (e.g., that the classical relativistic Hamilton–Jacobi equation is equivalent to a DHE satisfied by a particular class of DHSF) to obtain the correct relativistic quantum potential when the Dirac theory is interpreted as a de Broglie–Bohm theory. Some results appearing in the literature on this issue are criticized and the origin of some misconceptions is detailed with a rigorous mathematical analysis. Advances in Applied Clifford Algebras Springer Journals

The Dirac–Hestenes Equation and its Relation with the Relativistic de Broglie–Bohm Theory

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Springer International Publishing
Copyright © 2017 by Springer International Publishing
Physics; Mathematical Methods in Physics; Theoretical, Mathematical and Computational Physics; Applications of Mathematics; Physics, general
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