Pseudo-Hermitian Interactions in Dirac Theory: Examples

Abstract

We consider a couple of examples to study the pseudo-Hermitian interaction in relativistic quantum mechanics. Rasbha interaction, commonly used to study the spin Hall effect, is considered with imaginary coupling. The corresponding Dirac Hamiltonian is shown to be parity pseudo-Hermitian. In the other example we consider parity pseudo-Hermitian scalar interaction with arbitrary parameter in Dirac theory. In both the cases we show that the energy spectrum is real and all the other features of non-relativistic pseudo-Hermitian formulation are present. Using the spectral method the positive definite metric operator ($\eta$) has been calculated explicitly for both the models to ensure positive definite norms for the state vectors.

13 pages, Latex, No figs, Revised version to appear in MPLA

References in corpus (6)

• On A Proper Definition of Spin Current
• Equivalence of a Complex $\cP\cT$-Symmetric Quartic Hamiltonian and a Hermitian Quartic Hamiltonian with an Anomaly
• Quantum Mechanics of Klein-Gordon Fields I: Hilbert Space, Localized States, and Chiral Symmetry
• $(1+1)$ dimensional Dirac equation with non Hermitian interaction
• On some meaningful inner product for real Klein-Gordon fields with positive semi-definite norm
• Non-local PT-symmetric potentials in the one-dimensional Dirac equation

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• Critical coupling and coherent perfect absorption for ranges of energies due to a complex gain and loss symmetric system
• $\mathcal{P}\mathcal{T}$ Symmetric Hamiltonian Model and Dirac Equation in 1+1 dimensions
• Deconstructing non-dissipative non-Dirac-hermitian relativistic quantum systems
• Dirac equation with complex potentials
• Non-Hermitian $\mathcal{P}\mathcal{T}$-symmetric relativistic Quantum mechanics with a maximal mass in an external magnetic field
• Pseudo Hermitian interactions in the Dirac Equation
• Time Optimal Quantum Control of Spinor States
• Pseudo-Hermitian and PT -symmetric quantum systems with energy-dependent potentials: Bound-state solutions and energy spectra
• Physical constraints on effective non-Hermitian systems
• Quantum phase transitions and entanglement entropy in a non-Hermitian Jaynes-Cummings model