• DOI:10.1142/S0219887815500127
• Corpus ID: 119687416

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}
}

• L. Fatibene, R. McLenaghan, G. Rastelli
• 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 to the the second order operator that arises from that obtained from the unique separation scheme associated with such operators. It shown by the study of several examples that the operators arising from these two approaches coincide.