Investigation of Superluminal Motion of Free Spin-half Particles in Spacetime
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Date
2016-07
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KNUST
Abstract
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 ψ (x,t) is considered as a “classical field” 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 fiber bundle formalism.
Description
A thesis submitted to the Department of Mathematics, College of Science in partial fulfilment of the requirements for the degree of Doctor of Philosophy