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

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AUGUST, 2016
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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 SL(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 SL (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 \positive energy" and utilize the free Dirac waves propagating in the z􀀀direction. The Dirac wave function (x; t) is considered as a \classical fi eld" and the corresponding wave equation is derived from a symmetrized Lagrange function. 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 generalized translational relative velocity component of a free spin-half field indeed exceeds the speed of light. This result is also feasible in a fi ber bundle formalism.
A thesis submitted to the Department of Mathematics,College of Science, in partial ful llment of the requirements for the degree of Doctor of Philosophy,