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

Authors : Mustafa DERNEK, Semra GÜRTAŞ DOĞAN, Yusuf SUCU, Nuri ÜNAL

Pages : 509-526

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Publication Date : 0000-00-00

Article Type : Research Paper

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 SOinsert ignore into journalissuearticles values(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, QED 2 1, Pair production, Noether charge