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Advances in High Energy Physics
Volume 2015 (2015), Article ID 484151, 8 pages
http://dx.doi.org/10.1155/2015/484151
Research Article

Non-Hermitian Dirac Hamiltonian in Three-Dimensional Gravity and Pseudosupersymmetry

Department of Physics, Faculty of Science, Gazi University, 06500 Ankara, Turkey

Received 13 August 2015; Accepted 4 November 2015

Academic Editor: Frank Filthaut

Copyright © 2015 Özlem Yeşiltaş. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. The publication of this article was funded by SCOAP3.

Abstract

The Dirac Hamiltonian in the -dimensional curved space-time has been studied with a metric for an expanding de Sitter space-time which is two spheres. The spectrum and the exact solutions of the time dependent non-Hermitian and angle dependent Hamiltonians are obtained in terms of the Jacobi and Romanovski polynomials. Hermitian equivalent of the Hamiltonian obtained from the Dirac equation is discussed in the frame of pseudo-Hermiticity. Furthermore, pseudosupersymmetric quantum mechanical techniques are expanded to a curved Dirac Hamiltonian and a partner curved Dirac Hamiltonian is generated. Using -pseudo-Hermiticity, the intertwining operator connecting the non-Hermitian Hamiltonians to the Hermitian counterparts is found. We have obtained a new metric tensor related to the new Hamiltonian.