dorsal/arxiv
View SchemaPseudo-Hermitian Interactions in Dirac Theory: Examples
| Authors | Bhabani Prasad Mandal, Saurabh Gupta |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0605233 |
| URL | https://arxiv.org/abs/quant-ph/0605233 |
| DOI | 10.1142/S0217732310032901 |
| Journal | Mod. Phys. Lett. A 25, 1723 (2010) |
| License | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ |
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.
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"abstract": "We consider a couple of examples to study the pseudo-Hermitian interaction in\nrelativistic quantum mechanics. Rasbha interaction, commonly used to study the\nspin Hall effect, is considered with imaginary coupling. The corresponding\nDirac Hamiltonian is shown to be parity pseudo-Hermitian. In the other example\nwe consider parity pseudo-Hermitian scalar interaction with arbitrary parameter\nin Dirac theory. In both the cases we show that the energy spectrum is real and\nall the other features of non-relativistic pseudo-Hermitian formulation are\npresent. Using the spectral method the positive definite metric operator\n($\\eta$) has been calculated explicitly for both the models to ensure positive\ndefinite norms for the state vectors.",
"arxiv_id": "quant-ph/0605233",
"authors": [
"Bhabani Prasad Mandal",
"Saurabh Gupta"
],
"categories": [
"quant-ph",
"hep-th"
],
"doi": "10.1142/S0217732310032901",
"journal_ref": "Mod. Phys. Lett. A 25, 1723 (2010)",
"license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
"title": "Pseudo-Hermitian Interactions in Dirac Theory: Examples",
"url": "https://arxiv.org/abs/quant-ph/0605233"
},
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