Klein-Gordon and Dirac gyroscopes

TL;DR

This paper develops covariant Klein-Gordon and Dirac equations for relativistic quantum rigid bodies, providing explicit wave functions and spectra, including asymmetric cases, and ensuring consistency with prior relativistic rigid body definitions.

Contribution

It introduces a covariant formulation of Klein-Gordon and Dirac operators for relativistic rigid bodies, extending previous classical models to quantum mechanics.

Findings

Explicit wave functions for Klein-Gordon and Dirac gyroscopes

Spectral analysis of relativistic rigid bodies

Inclusion of asymmetric Dirac gyroscope cases

Abstract

The formulation of a rigid body in relativistic quantum mechanics is studied. Departing from an alternate approach at the relativistic classical level, the corresponding Klein-Gordon and Dirac operators for the rigid body are obtained in covariant form. The resulting wave equations are shown to be consistent, by construction, with earlier definitions of a relativistic rigid body by Aldinger et al (1983). Wave functions and spectra for both cases are obtained explicitly, including the Dirac gyroscope with asymmetries.