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Open Quantum Systems Decoherence Quantum Simulation

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

arXiv
Authors: Lorenzo Fatibene, Raymond G. McLenaghan, Giovanni Rastelli

Year

2014

Paper ID

8245

Status

Preprint

Abstract Read

~2 min

Abstract Words

110

Citations

N/A

Abstract

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.

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  • 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...

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References & Citation Signals

[1] DOI https://doi.org/arXiv:1407.4855 [2] arXiv https://arxiv.org/abs/1407.4855 [3] Publisher https://arxiv.org/abs/1407.4855

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