Second order symmetry operators for the massive Dirac equation. (English) Zbl 1518.83093
Summary: Employing the covariant language of two-spinors, we find what conditions a curved four-dimensional 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.
MSC:
| 83F05 | Relativistic cosmology |
| 81R20 | Covariant wave equations in quantum theory, relativistic quantum mechanics |
| 81R25 | Spinor and twistor methods applied to problems in quantum theory |
| 70F05 | Two-body problems |
| 22E70 | Applications of Lie groups to the sciences; explicit representations |
| 53C21 | Methods of global Riemannian geometry, including PDE methods; curvature restrictions |
| 53C50 | Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics |
| 83C27 | Lattice gravity, Regge calculus and other discrete methods in general relativity and gravitational theory |
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