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

Abstract

In this study, we introduce a relativistic quantum mechanical wave equation of the spin-1 particle as anexcited state of the zitterbewegung and show that it is consistent with the 2 + 1 dimensional Proca theory. At thesame time, we see that in the rest frame, this equation has two eigenstates; particle and antiparticle states or negativeand positive energy eigenstates, respectively, and satisfy SO(2,1) spin algebra. As practical applications, we derive theexact solutions of the equation in the presence of a constant magnetic field and a curved spacetime background. Fromthese solutions, we find Noether charge by integrating the zeroth component of the spin-1 particle current, called chargedensity, on hyper surface and discuss pair production from this charge. And, we see that the discussion on the Noethercharge is a useful tool for understanding the pair production phenomenon because it is derived from a probabilisticparticle current.