Second order symmetry operators for the massive Dirac equation
General Relativity and Quantum Cosmology
2023-02-02 v1
Abstract
Employing the covariant language of two-spinors, we find what conditions a curved Lorentzian spacetime must satisfy for existence of a second order symmetry operator for the massive Dirac equation. The conditions are formulated as existence of a set of Killing spinors satisfying a set of covariant linear differential equations. Using these Killing spinors, we then state the most general form of such an operator. Partial results for the zeroth and first order are presented and interpreted as well. Computer algebra tools from the Mathematica package suite xAct were used for the calculations.
Cite
@article{arxiv.2210.05216,
title = {Second order symmetry operators for the massive Dirac equation},
author = {Simon Jacobsson and Thomas Bäckdahl},
journal= {arXiv preprint arXiv:2210.05216},
year = {2023}
}
Comments
16 pages