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

2015/09/29 by Ozlem Yeşiltaş, Yeşiltaş, Ozlem
Mathematics · Physics and Astronomy · #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #hep-th #math-ph #math.MP

paper · pdf · doi:10.48550/arxiv.1509.08831

arxiv created 2015/09/29 · arxiv updated 2015/09/30

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 η-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.

Related

• Hermiticity of the Dirac Hamiltonian in Curved Spacetime
• Quantum mechanics for three versions of the Dirac equation in a curved spacetime
• Metric-induced non-Hermitian physics
• Dirac Equation In The Curved Spacetime and Generalized Uncertainty Principle: A fundamental quantum mechanical approach with energy dependent potentials
• The η-pseudo-hermitic generator in the deformed Woods Saxons potential