Remarks on the ($2+1$)-dimensional Duffin-Kemmer-Petiau oscillator in an external magnetic field

Abstract

This work re-examines the issue of spin-$1$ particles in a ($2+1$)-dimensional Duffin-Kemmer-Petiau oscillator (DKPO) in the presence of an external magnetic field. By following the appropriate procedure for the spin-$1$ sector of the Duffin-Kemmer-Petiau (DKP) theory, the previously used $6\times 6$ representation in the literature is shown to be reducible to a $3\times 3$ irreducible representation. This approach enabled us to find new aspects of the results recently disseminated in various studies, as well as other considerations overlooked and requiring revision. Finally, we present some applications of two-dimensional DKP theory in condensed matter systems, particularly in Lieb lattices.

07 pages, 4 figures

References in corpus (4)

• Quantum dynamics of scalar bosons in a cosmic string background
• Corroborating the equivalence between the Duffin-Kemmer-Petiau and the Klein-Gordon and Proca equations
• Splitting frequency of the (2+1)-dimensional Duffin-Kemmer-Petiau oscillator in an external magnetic field
• Comment on "Chern-Simons theory and atypical Hall conductivity in the Varma phase''