More about the S=1 relativistic oscillator

TL;DR

This paper introduces the S=1 Proca oscillator, a relativistic oscillator model for spin-1 particles, deriving its quantization rules and extending the approach to a two-body relativistic oscillator system.

Contribution

It develops the S=1 Proca oscillator using the Bargmann-Wigner framework and extends the methodology to a two-body relativistic oscillator system, revealing unique quantization rules.

Findings

Quantization rule: E =  \u03c9 for parity states (-1)^j

Quantization rule: E = \u00b1 \u03c9 (j+1/2) for parity states -(-1)^j

No radial excitations observed in the system

Abstract

Following to the lines drawn in my previous paper about the S=0 relativistic oscillator I build up an oscillatorlike system which can be named as the S=1 Proca oscillator. The Proca field function is obtained in the framework of the Bargmann-Wigner prescription and the interaction is introduced similarly to the S=1/2 Dirac oscillator case regarded by Moshinsky and Szczepaniak. We obtained the intriguing rule of quantization: E = \hbar \omega /2 for the parity states (-1)^j and E = \pm \hbar \omega (j+1/2) for the parity states -(-1)^j. There are no radial excitations. Finally, I apply the above-mentioned procedure to the case of the two-body relativistic oscillator.