Superluminal Motion of Free Spin-half Particles in a Fiber Bundle Formalism

The hypothesis of the spin of an electron, leading to its angular momentum, is no longer an open question, in science. Experimental evidence like the hydrogen fine structure and the Stern-Gerlach experiment in the 1920s and, recently, Nuclear Magnetic Resonance (NMR) have for long paved the way to definitely end this debate. Equipped with this mathematical machinery potent enough to handle the theories which are of interest to us, the expectation value of the overall relative linear velocity component of a fermion field was investigated in a previous paper, found quantized, and exceeding the speed of light. In the present article, we aim to review and describe this result in the framework of a fiber bundle theory. Using a method developed in the 1980s by Zimmer for Dynamical-System theory, we explicate the feasibility of the superluminal free electron and neutrino result in bundle language.