Symmetries and Supersymmetries of the Dirac-Type Operators on Curved Spaces
نویسنده
چکیده
The role of the Killing–Yano tensors in the construction of the Dirac-type operators is pointed out. The general results are applied to the case of the four-dimensional Euclidean Taub–Newman–Unti–Tamburino space. Three new Dirac-type operators, equivalent to the standard Dirac operator, are constructed from the covariantly constant Killing–Yano tensors of this space. Finally the Runge–Lenz operator for the Dirac equation in this background is expressed in terms of the fourth Killing–Yano tensor that is not covariantly constant.
منابع مشابه
ar X iv : h ep - t h / 04 11 01 6 v 1 1 N ov 2 00 4 Symmetries and supersymmetries of the Dirac operators in curved spacetimes
It is shown that the main geometrical objects involved in all the symmetries or supersymmetries of the Dirac operators in curved manifolds of arbitrary dimensions are the Killing vectors and the Killing-Yano tensors of any ranks. The general theory of external symmetry transformations associated to the usual isometries is presented, pointing out that these leave the standard Dirac equation inva...
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It is shown that the main geometrical objects involved in all the symmetries or supersymmetries of the Dirac operators in curved manifolds of arbitrary dimensions are the Killing vectors and the Killing-Yano tensors of any ranks. The general theory of external symmetry transformations associated to the usual isometries is presented, pointing out that these leave the standard Dirac equation inva...
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