# Symmetry operators and separation of variables for Dirac's equation on two-dimensional spin manifolds with external fields

```@article{Fatibene2014SymmetryOA,
title={Symmetry operators and separation of variables for Dirac's equation on two-dimensional spin manifolds with external fields},
author={Lorenzo Fatibene and Raymond G. McLenaghan and Giovanni Rastelli},
journal={arXiv: Mathematical Physics},
year={2014}
}```
• Published 17 July 2014
• Mathematics
• arXiv: Mathematical Physics
The second order symmetry operators that commute with the Dirac operator with external vector, scalar and pseudo-scalar potentials are computed on a general two-dimensional spin-manifold. It is shown that the operator is defined in terms of Killing vectors, valence two Killing tensors and scalar fields defined on the background manifold. The commuting operator that arises from a non-trivial Killing tensor is determined with respect to the associated system of Liouville coordinates and compared…

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