ar X iv : h ep - t h / 03 01 10 8 v 2 1 6 O ct 2 00 3 Symmetries of the Dirac operators associated with covariantly constant Killing - Yano tensors
نویسنده
چکیده
The continuous and discrete symmetries of the Dirac-type operators produced by particular Killing-Yano tensors are studied in manifolds of arbitrary dimensions. The Killing-Yano tensors considered are covariantly constant and realize certain square roots of the metric tensor. Such a Killing-Yano tensor produces simultaneously a Dirac-type operator and the generator of a one-parameter Lie group connecting this operator with the standard Dirac one. The Dirac operators are related among themselves through continuous or discrete transformations. It is shown that the groups of the continuous symmetry can be only U(1) and SU(2), specific to (hyper-)Kähler spaces, but arising even in cases when the requirements for these special geometries are not fulfilled. The discrete symmetries are also studied obtaining the discrete groups Z4 and Q. The briefly presented examples are the Euclidean Taub-NUT space and the Minkowski spacetime. Pacs 04.62.+v
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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
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متن کاملar X iv : h ep - t h / 04 11 01 6 v 2 2 5 Fe b 20 08 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...
متن کاملSymmetries of the Dirac operators associated with covariantly constant Killing - Yano tensors
The continuous and discrete symmetries of the Dirac-type operators produced by particular Killing-Yano tensors are studied in manifolds of arbitrary dimensions. The Killing-Yano tensors considered are covariantly constant and realize certain square roots of the metric tensor. Such a Killing-Yano tensor produces simultaneously a Dirac-type operator and the generator of a one-parameter Lie group ...
متن کاملSymmetries and Supersymmetries of the Dirac-Type Operators on Curved Spaces
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تاریخ انتشار 2008