A generally-relativistic gauge classification of the Dirac fields

Abstract

We consider generally-relativistic gauge transformations for the spinorial fields finding two mutually exclusive but together exhaustive classes in which fermions are placed adding supplementary information to the results obtained by Lounesto, and identifying quantities analogous to the momentum vector and the Pauli-Lubanski axial vector we discuss how our results are similar to those obtained by Wigner; by taking into account the system of Dirac field equations we will investigate the consequences for the dynamics: and in particular we shall address the problem of getting the non-relativistic approximation in a consistent way. We are going to comment on extensions.

7 pages

References in corpus (5)

• Classification of Singular Spinor Fields and Other Mass Dimension One Fermions
• Exotic Dark Spinor Fields
• Bilinear Covariants and Spinor Fields Duality in Quantum Clifford Algebras
• The quadratic spinor Lagrangian, axial torsion current, and generalizations
• Questing for Algebraic Mass Dimension One Spinor Fields

Cited by in corpus (38)

• On the Spinor Representation
• Torsion Gravity for Dirac Fields
• Spinors in Polar Form
• Covariant Inertial Forces for Spinors
• General Dynamics of Spinors
• The emergence of flagpole and flag-dipole fermions in fluid/gravity correspondence
• Weyl and Majorana Spinors as Pure Goldstone Bosons
• Polar Form of Spinor Fields from Regular to Singular: the Flag-Dipoles
• Fundamental Theory of Torsion Gravity
• Polar solutions with tensorial connection of the spinor equation
• Spinor Fields, Singular Structures, Charge Conjugation, ELKO and Neutrino Masses
• Unveiling a spinor field classification with non-Abelian gauge symmetries
• Geometry, Zitterbewegung, Quantization
• ELKO in Polar Form
• Torsion Axial Vector and Yvon-Takabayashi Angle: Zitterbewegung, Chirality and all that
• The role of singular spinor fields in a torsional gravity, Lorentz-violating, framework
• The Heisenberg spinor field classification and its interplay with the Lounesto's classification
• Hearing the shape of inequivalent spin structures and exotic Dirac operators
• Non-Trivial Effects of Sourceless Forces for Spinors: Toward an Aharonov-Bohm gravitational effect?
• New fermions in the bulk
• New spinor classes on the Graf-Clifford algebra
• A Square-Integrable Spinor Solution to Non-Interacting Dirac Equations
• A geometrical assessment of spinorial energy conditions
• Axially-Symmetric Exact Solutions for Flagpole Fermions with Gravity
• Torsion Gravity for Dirac Particles
• The Tensorial Connections
• Re-normalizable Chern-Simons Extension of Propagating Torsion Theory
• Dirac spinors and their application to Bianchi-I space-times in 5 dimensions
• The most complete mass-dimension four topological gravity
• Decoherence-Free Entropic Gravity for Dirac Fermion
• Cross section for Bhabha and Compton scattering beyond quantum field theory
• Additional fermionic fields onto parallelizable 7-spheres
• Non-existence of rest-frame spin-eigenstate spinors in their own electrodynamics
• Polar analysis of the Dirac equation through dimensions
• Necessity of Tensorial Connections for Spinorial Systems
• Chern-Simons Extension of ESK Theory
• The Most General Propagator in Quantum Field Theory
• Angular-Radial Integrability of Coulomb-like Potentials in Dirac Equations