The Duffin-Kemmer-Petiau oscillator in the presence of minimal uncertainty in momentum

Abstract

In the anti-de Sitter background, the position and momentum operators obey the extended commutation relations leading to the emergence of a minimal uncertainty in momentum. Here, by using the position space representation we exactly determine the energy eigenvalues and the corresponding eigenfunctions for a (3+1) dimensional Duffin-Kemmer-Petiau oscillator of spin-zero and one in the framework of extended commutation relations.