Spinors in Polar Form

Abstract

Spinor fields are considered in a generally covariant environment where they can be written in the polar form. The polar form is the one in which spinorial fields are expressed as a module times the exponential of a complex pseudo-phase, and in this form the full spinorial field theory can in turn be expressed by employing only real tensorial quantities. Such a reformulation makes it possible to emphasize properties of the spinorial field theory, and this would enrich our understanding in ways that have never been followed up until this moment.

11 pages

References in corpus (3)

• Classification of Singular Spinor Fields and Other Mass Dimension One Fermions
• Bilinear Covariants and Spinor Fields Duality in Quantum Clifford Algebras
• Polar solutions with tensorial connection of the spinor equation

Cited by in corpus (20)

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• Dirac Theory in Hydrodynamic Form
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• Quantum solitodynamics: Non-linear wave mechanics and pilot-wave theory
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• Dirac hydrodynamics in 19 forms
• Relativistic dynamical inversion in manifestly covariant form
• A Square-Integrable Spinor Solution to Non-Interacting Dirac Equations
• Torsionally-Induced Stability in Spinors
• Quantum hydrodynamics of spinning particles in electromagnetic and torsion fields
• Re-normalizable Chern-Simons Extension of Propagating Torsion Theory
• A note on singularity avoidance in fourth-order gravity
• The most complete mass-dimension four topological gravity
• General Spin Sums in Quantum Field Theory
• Necessity of Tensorial Connections for Spinorial Systems
• Symmetry Breaking of Universal type and Particular types
• Goldstone states as non-local hidden variables
• A note on hidden classes in spinor classification
• Integrability of Dirac equations in static spherical space-times
• Angular-Radial Integrability of Coulomb-like Potentials in Dirac Equations