Abstract
In this paper, by using the Dirac derivatives the Klein–Gordon (K-G) equation is determined in a [Formula: see text]-Minkowski spacetime. The dispersion relation and the first-order approximation case are deduced. The Feshbach–Villars (FV) equation is derived by applying the new linearization process to the time. We then study the effect of magnetic interaction on energies spectrum in a [Formula: see text]-Minkowski spacetime as an application, as a result we found that the energies spectrum are not symmetrical. We also study the case of hydrogen atom in non-relativistic limit by using perturbation theory. The upper bound of the [Formula: see text]-deformation parameter is evaluate, on the basis of the experimental data for [Formula: see text] transition frequency.
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