More about the $j=0$ relativistic oscillator

TL;DR

This paper develops a relativistic oscillator model for the $j=0$ case starting from Bargmann-Wigner equations, introducing a new interaction form, and deriving equations that differ from previous models, resulting in a distinct energy spectrum.

Contribution

It introduces a novel $j=0$ relativistic oscillator model based on the Bargmann-Wigner framework with a different interaction form, leading to new equations and energy spectra.

Findings

Derived new equations for the $j=0$ relativistic oscillator.

Found that the equations differ from previous models.

Resulted in a different energy spectrum for the system.

Abstract

I start from the Bargmann-Wigner equations and introduce an interaction in the form which is similar to a $j=1/2$ case [M. Moshinsky & A. Szczepaniak, {\it J. Phys. A}{\bf 22} (1989) L817]. By means of the expansion of the wave function in the complete set of $\gamma$- matrices one can obtain the equations for a system which could be named as the $j=0$ Kemmer-Dirac oscillator. The equations for the components $\phi_1$ and $\phi_2$ are different from the ones obtained by Y. Nedjadi & R. Barrett for the $j=0$ Duffin-Kemmer-Petiau oscillator [{\it J. Phys. A} {\bf 27} (1994) 4301]. This fact leads to the dissimilar energy spectrum of the $j=0$ relativistic oscillator.