In this study, we introduce a relativistic quantum mechanical wave equation of the spin-1 particle as an excited state of the zitterbewegung and show that it is consistent with the 2+1 dimensional Proca theory. At the same time, we see that in the rest frame this equation has two eigenstates, particle and antiparticle states or negative and positive energy eigenstates, respectively, and satisfy SO(2, 1) spin algebra. As practical applications, we derive the exact solutions of the equation in the presence of a constant magnetic field and a curved spacetime. From these solutions, we find Noether charge by integrating the constructed spin-1 particle current on hyper surface and discuss pair production from the charge. And, we see that the discussion on the Noether charge is useful tool for undersdantding the pair production phenomenon because the charge is derived from a probabilistic particle current.
We investigate the interaction of a generalized vector boson oscillator with the near-horizon geometry of the BTZ black hole and try to determine the corresponding quasibound state frequencies. To do this, we seek an analytical solution of the relativistic vector boson equation, derived as an excited state of Zitterbewegung, with Cornell-type non-minimal coupling in the near-horizon geometry of the BTZ black hole. The vector boson equation includes a symmetric spinor of rank two and this allows to obtain an analytical solution of the corresponding equation. By imposing appropriate boundary conditions, we show that it is possible to arrive at a relativistic frequency ($\omega$) expression in the form of $\omega=\omega_{\mathcal{R}e}+\omega_{\mathcal{I}m}$. Our results show that real($\propto \omega_{\mathcal{R}e}$) and damped($\propto \frac{1}{|\omega_{\mathcal{I}m}|}$) oscillations depend on the parameters of the background geometry, coefficients of the non-minimal coupling and strength of the oscillator. This allows us to analyse the effects of both non-minimal coupling and spacetime parameters on the evolution of the considered vector field. We discuss the results in details and see also that the background is stable under the perturbation field in question.
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