Abstract

The possibility of free spin-1/2 particles (also called Dirac particles)superluminal motion in spacetime, is investigated. The universal coverof the entire Lorentz group $\mathcal{L}$ consists of $SL\left(2,\mathbb{C}\right)$and the spinor map so that to obtain a relativistically invariantdescription of the state of an electron, one looks to the representationsof $SL\left(2,\mathbb{C}\right),$ that is, to the 2-valued representationof $\mathcal{L},$ known as spinors. We restrict our approach to realisticone-particle systems along with the ``positive energy'' and utilizethe free Dirac waves propagating in the $z-$direction. The Diracwave function $\psi\left(x,t\right)$ is considered as a ``classicalfield'' and the corresponding wave equation is derived from a Lagrangefunction. Using the symmetrized Dirac Lagrange density, it is observedthat variation in spin angular momentum (in the light cone) leadsto causality violation, whereas variation in orbital angular momentumdoes not. Consequently, it is shown that the expectation value of the relative translational velocitycomponent of the spinning free electron exceeds light speed.

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