Polar form of Dirac fields: implementing symmetries via Lie derivative

Abstract

We consider the Lie derivative along Killing vector fields of the Dirac relativistic spinors: by using the polar decomposition we acquire the mean to study the implementation of symmetries on Dirac fields. Specifically, we will become able to examine under what conditions it is equivalent to impose a symmetry upon a spinor or only upon its observables. For one physical application, we discuss the role of the above analysis for the specific spherical symmetry, obtaining some no-go theorem regarding spinors and discussing the generality of our approach.

10 pages

References in corpus (16)

• Particle-Like Solutions of the Einstein-Dirac Equations
• Asymptotically flat scalar, Dirac and Proca stars: discrete vs. continuous families of solutions
• Asymptotically flat spinning scalar, Dirac and Proca stars
• Non-Existence of Time-Periodic Solutions of the Dirac Equation in a Reissner-Nordstrom Black Hole Background
• Vacuum State of the Dirac Field in de Sitter Space and Entanglement Entropy
• Non-Existence of Black Hole Solutions for a Spherically Symmetric, Static Einstein-Dirac-Maxwell System
• Dirac star in the presence of Maxwell and Proca fields
• Constructing spherically symmetric Einstein-Dirac systems with multiple spinors: Ansatz, wormholes and other analytical solutions
• Spinor fields in spherical symmetry. Einstein-Dirac and other space-times
• The Lie derivative of spinor fields: theory and applications
• Reductive G-structures and Lie derivatives
• Boson and Dirac stars in $D\ge 4$ dimensions
• Weyl and Majorana Spinors as Pure Goldstone Bosons
• Polar Form of Spinor Fields from Regular to Singular: the Flag-Dipoles
• Spinor fields in spherically symmetric space-time
• Dirac hydrodynamics in 19 forms

Cited by in corpus (1)

• Euler and Pontryagin currents of the Dirac operator