Pseudo-Hermitian Interactions in Dirac Theory: Examples

Details Pseudo-Hermitian Interactions in Dirac Theory: Examples Pseudo-Hermitian Interactions in Dirac Theory: Examples

2006-05-29

arxiv.org/abs/quant-ph/0605233v3

Physics

Quantum Physics

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

Scientific paper

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.

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