Investigation of Superluminal Motion of Free Spin-half Particles in Spacetime

Emmanuel Gazoya, Francis Oduro, Edward Prempeh
2015 Journal of Mathematics Research  
The possibility of free spin-1/2 particles (also called Dirac particles) superluminal motion in spacetime, is investigated. The universal cover of the entire Lorentz group L consists of S L (2, C) and the spinor map so that to obtain a relativistically invariant description of the state of an electron, one looks to the representations of S L (2, C) , that is, to the 2-valued representation of L, known as spinors. We restrict our approach to realistic one-particle systems along with the
more » ... g with the "positive energy" and utilize the free Dirac waves propagating in the z−direction. The Dirac wave function ψ (x, t) is considered as a "classical field" and the corresponding wave equation is derived from a Lagrange function. Using the symmetrized Dirac Lagrange density, it is observed that variation in spin angular momentum (in the light cone) leads to causality violation, whereas variation in orbital angular momentum does not. Consequently, it is shown that the expectation value of the relative translational velocity component of the spinning free electron exceeds light speed.
doi:10.5539/jmr.v7n4p12 fatcat:wjzj2n6q7zeu3daphkmrclhoza