3D transformation for point rotating reference frames and localized neutrinos in a rotating electromagnetic field

TL;DR

This paper develops a non-Galilean transformation for Dirac's equation in rotating electromagnetic fields, revealing localized neutrino solutions with invariant spin and discussing their stability.

Contribution

It introduces a general non-Galilean transformation with a fundamental time constant, enabling stationary solutions and identifying localized neutrino states in rotating fields.

Findings

Existence of periodic, bounded solutions in rotating frames

Identification of massless localized neutrino states

Potential stability of resting frame states

Abstract

The problem of Dirac's equation in a rotating electromagnetic field can be reduced to the stationary by using a transformation for point rotating reference frames. The general form of the non-Galilean transformation is deduced in the paper. For the non-Galilean transformation time is different in the rotating and resting frame. This transformation contains a constant, with the dimension of time. The constant is assumed to be fundamental. The transformation forms the necessary condition for the existence of periodic, bounded and square integrable solutions in both the rotating and resting frame. Variety of such solutions exists. Among the solutions massless states are identified. They describe localized neutrinos with invariable spin. The states in the resting frame are not stationary but they have a good chance to be stable.