Noncommutative vector DKP oscillator in an external magnetic field

In this paper, we considered the solutions of the Duffin–Kemmer–Petiau oscillator for spin-1 particles in the noncommutative plane for states associated with the spin-projection numbers ±1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\pm 1$$\end{document}. We show that the space noncommutativity acts exactly as an external magnetic field, thus resulting in bounds on the corresponding energy eigenvalues and a lifting of their degeneracy. Then, we studied the result of applying an external magnetic field for the obtained solutions. Notably, we found that the limits on the energy placed by the space noncommutativity are removed for a critical value of the magnetic field. The interesting particular case of a spin-one particle moving in a NC plane under an external magnetic field as well as the non-relativistic limit of the model is also discussed.