Charged Dirac fermions with anomalous magnetic moment in the presence of the chiral magnetic effect and of a noncommutative phase space

In this paper, we analyze the relativistic energy spectrum (or relativistic Landau levels) for charged Dirac fermions with anomalous magnetic moment (AMM) in the presence of the chiral magnetic effect (CME) and of a noncommutative (NC) phase space, where we work with the $(3+1)$-dimensional Dirac equation in cylindrical coordinates. Using a similarity transformation, we obtain four coupled first-order differential equations. Subsequently, obtain four non-homogeneous second-order differential equations. To solve these equations exactly and analytically, we use a change of variable, the asymptotic behavior, and the Frobenius method. Consequently, we obtain the relativistic spectrum for the electron/positron, where we note that this spectrum is quantized in terms of the radial quantum number $n$ and the angular quantum number $m_j$, and explicitly depends on the position and momentum NC parameters $\theta$ and $\eta$ (describes the NC phase space), cyclotron frequency ${\omega }_c$ (an angular frequency that depends on the electric charge $e$, mass $m$, and external magnetic field $B$, i.e., ${\omega }_c=eB\mathrm{/}m$), anomalous magnetic energy $E_m$ (an energy generated through the interaction of the AMM with the external magnetic field), $z$-momentum $k_z$ (linear momentum along the $z$-axis), and on the fermion and chiral chemical potential $\mu$ and ${\mu }_5$ (describes the CME). However, through $\theta$, $\eta$, and $m$, we define two types of ‘‘NC angular frequencies’’, given by ${\omega }_{\theta }=4\mathrm{/}m\theta$ and ${\omega }_{\eta }=\eta \mathrm{/}m$ (our spectrum depends on three angular frequencies). Comparing our spectrum with other papers, we verified that it generalizes several particular cases found in the literature. Besides, we also graphically analyze the behavior of the spectrum as a function of $B$, $\mu$, ${\mu }_5$, $k_z$, $\theta$, and $\eta$ for three different values of $n$ and $m_j$.