Covariant Inertial Forces for Spinors

Abstract

In this paper we consider the Dirac spinor field in interaction with a background of electrodynamics and torsion-gravity; by performing the polar reduction we acquire the possibility to introduce a new set of objects that have the geometrical status of non-vanishing tensors but which seem to contain the same information of the connection: thus they appear to be describing something that seems like an inertial force but which is also essentially covariant. After a general introduction, we exemplify these tensors in the very well known instance of the orbital of minimal energy for an electron in the case of the Hydrogen atom: we will see that the invariants built with these tensors remain different from zero even for free field configurations. An outlook regarding possible interpretations of such a set of tensors will be sketched. A few final comments will eventually be given.

6 pages

References in corpus (5)

• Classification of Singular Spinor Fields and Other Mass Dimension One Fermions
• A generally-relativistic gauge classification of the Dirac fields
• Torsion Gravity for Dirac Fields
• General Dynamics of Spinors
• Torsion Axial Vector and Yvon-Takabayashi Angle: Zitterbewegung, Chirality and all that

Cited by in corpus (19)

• Spinors in Polar Form
• Weyl and Majorana Spinors as Pure Goldstone Bosons
• Polar Form of Spinor Fields from Regular to Singular: the Flag-Dipoles
• de Broglie-Bohm formulation of Dirac fields
• Geometry, Zitterbewegung, Quantization
• ELKO in Polar Form
• Non-Trivial Effects of Sourceless Forces for Spinors: Toward an Aharonov-Bohm gravitational effect?
• A Square-Integrable Spinor Solution to Non-Interacting Dirac Equations
• The Tensorial Connections
• The most complete mass-dimension four topological gravity
• Re-normalizable Chern-Simons Extension of Propagating Torsion Theory
• Decoherence-Free Entropic Gravity for Dirac Fermion
• Cross section for Bhabha and Compton scattering beyond quantum field theory
• Necessity of Tensorial Connections for Spinorial Systems
• Madelung Structure of the Dirac Equation
• Polar analysis of the Dirac equation through dimensions
• Chern-Simons Extension of ESK Theory
• The Most General Propagator in Quantum Field Theory
• Angular-Radial Integrability of Coulomb-like Potentials in Dirac Equations