Relativistic quantum mechanical spin-1 wave equation in 2 + 1 dimensional spacetime

Authors: MUSTAFA DERNEK, SEMRA GÜRTAŞ DOĞAN, YUSUF SUCU, NURİ ÜNAL

Abstract: 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 background. From these solutions, we find Noether charge by integrating the zeroth component of the spin-1 particle current, called charge density, on hyper surface and discuss pair production from this charge. And, we see that the discussion on the Noether charge is a useful tool for understanding the pair production phenomenon because it is derived from a probabilistic particle current.

Keywords: Spin-1 particle wave equation, Gravity, QED₂₊₁ , Pair production, Noether charge

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