Supersymmetry and discrete transformations of the Dirac operators in Taub-NUT geometry
arXiv:hep-th/0202034 · doi:10.1023/A:1022365731912
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.
14 pages, latex, no figures
References in corpus (7)
- On the existence of the second Dirac operator in Riemannian space
- Schrödinger quantum modes on the Taub-NUT background
- The Dirac equation in Taub-NUT space
- Runge-Lenz operator for Dirac field in Taub-NUT background
- Dynamical algebra and Dirac quantum modes in Taub-NUT background
- The Dirac field in Taub-NUT background
- Hierarchy of Dirac, Pauli and Klein-Gordon conserved operators in Taub-NUT background