Abstract
We translate the Dirac equation into the Clifford algebra of physical space. We study the second-order equation, the relativistic invariance, the gauge invariance, the Lagrangian density and the tensors of the Dirac theory. Next we completely solve, by separation of variables, the Dirac equation for the hydrogen atom. The classical solutions have vanishing invariants and we calculate some linear combinations of the classical solutions with nonvanishing invariants. These solutions may be the linear approximations for a nonlinear equation previously studied.
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Daviau, C. (1998). Dirac Equation in the Clifford Algebra of Space. In: Dietrich, V., Habetha, K., Jank, G. (eds) Clifford Algebras and Their Application in Mathematical Physics. Fundamental Theories of Physics, vol 94. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-5036-1_8
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DOI: https://doi.org/10.1007/978-94-011-5036-1_8
Publisher Name: Springer, Dordrecht
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