Spinless Duffin-Kemmer-Petiau Oscillator in a Galilean Non-commutative Phase Space

Abstract

We examine Galilei-invariant linear wave equations in a non-commutative phase space. Specifically, we establish and solve the Galilean covariant Duffin-Kemmer-Petiau equation for spin-0 fields in a harmonic oscillator potential. We obtain these wave equations with a Galilean covariant approach, based on a (4+1)-dimensional manifold with light-cone coordinates followed by a reduction to a 3+1)-dimensional spacetime. We find the exact wave functions and their energy levels, and we examine the effects of non-commutativity.