Klein–Gordon and Dirac gyroscopes

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 Phys. Rev. D 28 3020). Wavefunctions and spectra for both cases are obtained explicitly, including the Dirac gyroscope with asymmetries.

Fundamental constraints on two-time physics

“…Some nice results regarding this topic were summarized in [24](in particular, Chapter XII, 315-316), especially those connected with the many-body Dirac oscillator. For more recent applications to spectroscopy of relativistic composites, see [25,26], where similar ideas came into play for strongly interacting relativistic particles. The treatment in [25], eqns.…”

Schematic baryon models, their tight binding description and their microwave realization

“…Taking up a suggestion made by one of the authors in a previous paper [38] to use a relativistic rotor or gyroscope as a schematic model for baryons, we have emulated such a system in a microwave setup after mapping it onto a chain of resonators consistent of dimers with successively decreasing coupling. This was implemented by increasing distances between resonators, taking advantage of the fact that the selected TE mode was evanescent between the resonators for the selected distance of the covering plate.…”

“…Based on three postulates for rigidity in a relativistic context [34][35][36][37] given below, one of the authors has studied [38] a relativistic quantum rotor denominated Dirac gyroscope. It generalizes the Dirac equation to a particle with internal structure.…”

“…In the body-fixed frame of reference 7 , the corresponding Hamiltonian is given by [38] where M is the rest mass of the body, α, β are Dirac matrices in the laboratory frame,…”

“…zz is the inverse square root of the inertia tensor and L is the orbital angular momentum vector in the body frame. In equation (24) of [38] it was also shown that the corresponding Dirac equation in the body frame leads to a tractable eigenvalue problem when the body has axial symmetry. In the fully asymmetric case, on the other hand, one has to rely on matrix diagonalization methods.…”