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Supersymmetry and discrete transformations of the Dirac operators in Taub-NUT geometry

Ion I. Cotăescu·Mihai Visinescu
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Abstract

It is shown that the N=4 superalgebra of the Dirac theory in Taub-NUT space has different unitary representations related among themselves through unitary U(2) transformations. In particular the SU(2) transformations are generated by the spin-like operators constructed with the help of the same covariantly constant Killing-Yano tensors which generate Dirac-type operators. A parity operator is defined and some explicit transformations which connect the Dirac-type operators among themselves are given. These transformations form a discrete group which is a realization of the quaternion discrete group. The fifth Dirac operator constructed using the non-covariant Killing-Yano tensor of the Taub-NUT space is quite special. This non-standard Dirac operator is connected with the hidden symmetry and is not equivalent to the Dirac-type operators of the standard N=4 supersymmetry.

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Ion I. Cotăescu, Mihai Visinescu. 2002-02-06. Supersymmetry and discrete transformations of the Dirac operators in Taub-NUT geometry. https://doi.org/10.1023/a%3A1022365731912

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