The Dirac-Hestenes Equation for Spherical Symmetric Potentials in the Spherical and Cartesian Gauges

Details The Dirac-Hestenes Equation for Spherical Symmetric Potentials in the Spherical and Cartesian Gauges The Dirac-Hestenes Equation for Spherical Symmetric Potentials in the Spherical and Cartesian Gauges

2006-01-09

arxiv.org/abs/math-ph/0601018v2

Int.J.Mod.Phys.A21 (2006) 4071-4082

Physics

Mathematical Physics

13 pages, accepted for publication in Int.J.Mod.Phys.A

Scientific paper

10.1142/S0217751X06033106

In this paper using the apparatus of the Clifford bundle formalism we show how straightforwardly solve in Minkowski spacetime the Dirac-Hestenes equation -- which is an appropriate representative in the Clifford bundle of differential forms of the usual Dirac equation -- by separation of variables for the case of a potential having spherical symmetry in the Cartesian and spherical gauges. We show that contrary to what is expected at a first sight, the solution of the DHE in both gauges has exactly the same mathematical difficulty.

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