Real spectra for the non-Hermitian Dirac equation in 1+1 dimensions with the most general coupling

2009/03/23 by V. G. C. S. dos Santos, A. de Souza Dutra, Marcelo Hott +1 · 1 citation
Mathematics · Physics and Astronomy · #Dirac (video compression format) #Dirac equation #Geometry #Hermitian matrix #Mathematical physics #Mathematics #Neutrino #Physics #Pseudoscalar #Quantum Mechanics and Non-Hermitian Physics #Quantum chaos and dynamical systems #Quantum mechanics #Scalar (mathematics) #math-ph #math.MP #quant-ph

paper · pdf · doi:10.1016/j.physleta.2009.07.054

11 pages

arxiv created 2009/03/23 · openalex publication_date 2009/07/24 · arxiv updated 2015/05/13 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

The most general combination of couplings of fermions with external potentials in 1+1 dimensions, must include vector, scalar and pseudoscalar potentials. We consider such a mixing of potentials in a PT-symmetric time-independent Dirac equation. The Dirac equation is mapped into an effective PT-symmetric Schrödinger equation. Despite the non-hermiticity of the effective potential, we find real energies for the fermion.

Citations

• sl(2, ) as a complex Lie algebra and the associated non-Hermitian Hamiltonians with real eigenvalues
• A simple action for a free fractional spin particle
• Making sense of non-Hermitian Hamiltonians
• (1+1)-Dirac Particle with Position-Dependent Mass in Complexified Lorentz Scalar Interactions: Effectively PT -Symmetric
• Real Spectra in Non-Hermitian Hamiltonians HavingPTSymmetry
• Relativistic supersymmetric quantum mechanics based on Klein–Gordon equation
• Supersymmetry and Quantum Mechanics
• Bounded solutions of fermions in the background of mixed vector-scalar Pöschl-Teller–like potentials
• Complex Extension of Quantum Mechanics
• Pseudo-Hermiticity of Hamiltonians under imaginary shift of the coordinate: real spectrum of complex potentials

Cited by

• Dirac equation in low dimensions: The factorization method