Classical Limit and Ehrenfest’s Theorem Versus Non-relativistic Limit of Noncommutative Dirac Equation in the Presence of Minimal Uncertainty in Momentum

In this article, we discuss the classic limit and investigate the Ehrenfest’s theorem of the Dirac equation in the context of minimal uncertainty in momentum within a noncommutative setting, and examine its \(\mathcal {CPT}\) symmetry and Lorentz symmetry violation. Also, we study the non-relativistic limit of this Dirac system, which leads to obtain a deformed Schrödinger–Pauli equation. Besides we check if this obtained equation still show explicitly the gyromagnetic factor of the electron. Interestingly, the overlap and congruence aspects of the classical and non-relativistic limits of the Dirac equation are clarified. The effects of both minimal uncertainty in momentum and noncommutativity on the Ehrenfest’s theorem and non-relativistic limit are well examined. Knowing that with both the linear Bopp–Shift and \(\star \)product, the noncommutativity is inserted.