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.

The DKP oscillator with a linear interaction in the cosmic string space-time

“…A generalized bosonic oscillator within the minimal length quantum mechanics has been analyzed in [29]. De Melo et al released a higherdimensional formulation of Galilean covariance to consider the noncommutative DKP oscillator [30]. Falek and Merad presented both spin-zero and spinone DKP equations in noncommutative space in the (1 + 3)-dimensional case [31].…”

Dirac Oscillator in a Galilean Covariant Non-commutative Space

“…The purpose of this paper is to apply 'Galilean covariance' (a formulation of non-relativistic theory exploiting covariant equations in higher dimension) to study the non-relativistic Dirac oscillator in a non-commutative space. This paper is the direct continuation of our previous study of the Galilean covariant Duffin-Kemmer-Petiau (DKP) spin-zero oscillator in a noncommutative space [1]. The DKP equation is a first-order wave equation which describes spin-zero and spin-one particles (see Refs.…”

“…This has the same form as Eq. ( 32) of our previous article on the spin-zero DKP oscillator [1]. Accordingly, let us introduce the function f (y), related to u(y) through…”

“…As the spinless DKP oscillator [1], its solution is the confluent hypergeometric function (see Sect. 13.1.1 of Ref.…”

The Statistical Properties of Spin-One DKP Oscillator under an External Magnetic Field in Noncommutative Space

“…Typical examples of such cases include an open string attached to -branes in the presence of background B-field inducing noncommutativity in its both end points [12][13][14][15], the quantum Hall effect [16] and the DKP oscillator [17]. The interface with solid-state physics and semiconductor theories are also studied in [17][18][19][20].…”