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

Andrés G. Jirón, Luis B. Castro, Angel E. Obispo, Antonio S. de Castro

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.

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

Abstract

This work re-examines the issue of spin- particles in a ()-dimensional Duffin-Kemmer-Petiau oscillator (DKPO) in the presence of an external magnetic field. By following the appropriate procedure for the spin- sector of the Duffin-Kemmer-Petiau (DKP) theory, the previously used representation in the literature is shown to be reducible to a 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.
Paper Structure (9 sections, 53 equations, 3 figures)

This paper contains 9 sections, 53 equations, 3 figures.

Table of Contents

  1. INTRODUCTION
  2. The Duffin-Kemmer-Petiau equation
  3. ($2+1$)-dimensional DKP equation
  4. DKP oscillator in a magnetic field
  5. Particular cases
  6. DKPO in ($2+1$) dimensions
  7. Uniform magnetic field in ($2+1$) dimensions
  8. Two-dimensional DKP prescription and the connection with condensed matter physics
  9. Conclusions

Figures (3)

  • Figure 1: Plots of the energy as a function of $\omega$ and different values of $n$ and $l$, with $m=1$. The dotted line represents the constraints $\epsilon_{+}$ and $\epsilon_{-}$.
  • Figure 2: Plots of the energy as a function of $\tilde{\omega}$ and different values of $n$ and $l$, with $m=1$. The dotted line represents the constraints $\epsilon_{+}$ and $\epsilon_{-}$.
  • Figure 3: Lieb lattice