Non-Hermitian Dirac Hamiltonian in three dimensional gravity and pseudo-supersymmetry

TL;DR

This paper explores the properties of a non-Hermitian Dirac Hamiltonian in a curved (2+1)D spacetime, deriving solutions, Hermitian equivalents, and extending pseudo-supersymmetry techniques in a gravitational context.

Contribution

It introduces a novel approach to analyze non-Hermitian Dirac Hamiltonians in curved spacetime using pseudo-Hermiticity and pseudo-supersymmetry, including new metrics and solution methods.

Findings

Exact solutions in terms of Jacobi and Romanovski polynomials

Hermitian equivalents via pseudo-Hermiticity

Extension of pseudo-supersymmetry to curved spacetime

Abstract

The Dirac Hamiltonian in the (2+1) dimensional curved space-time has been studied with a metric for an expanding de Sitter space-time which is a two sphere. 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, pseudo-supersymmetric quantum mechanical techniques are expanded to a curved Dirac Hamiltonian and a partner curved Dirac Hamiltonian is generated. Using \eta-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.