Second order symmetry operators for the massive Dirac equation
arXiv:2210.05216 · doi:10.1088/1361-6382/acb3a9
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.
arXiv comment16 pages
References in corpus (8)
- Dirac symmetry operators from conformal Killing-Yano tensors
- Quantum Mechanics of Yano tensors: Dirac equation in curved spacetime
- Commuting symmetry operators of the Dirac equation, Killing-Yano and Schouten-Nijenhuis brackets
- Second order symmetry operators
- First-order symmetries of Dirac equation in curved background: a unified dynamical symmetry condition
- Second Order Symmetries of the Conformal Laplacian
- Second order symmetry operators for the massive Dirac equation
- A space-time calculus based on symmetric 2-spinors