Response tensor for a spin-dependent electron gas: dependence on the choice of spin operator

It is shown that the choice of spin-operator affects the form of the response tensor describing a spin-dependent electron gas. The covariant, spin-dependent response tensor for a magnetic dipole moment-polarized electron gas (statistical distribution of electrons and positrons) is evaluated. A simul...

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Bibliographic Details
Published in:arXiv.org 2021-04
Main Authors: Demcsak, Victor M, Melrose, Donald B
Format: Article
Language:English
Subjects:
Dependence
Dipole moments
Eigenvectors
Electron gas
Electron spin
Electrons
Helicity
Magnetic dipoles
Mathematical analysis
Optical activity
Plasmas
Positrons
Tensors
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Summary:It is shown that the choice of spin-operator affects the form of the response tensor describing a spin-dependent electron gas. The covariant, spin-dependent response tensor for a magnetic dipole moment-polarized electron gas (statistical distribution of electrons and positrons) is evaluated. A simultaneous eigenfunction of both the magnetic-moment spin-operator and the Dirac Hamiltonian is constructed, from which explicit expressions for the magnetic-moment states and the corresponding vertex functions are derived. It is shown that a gas of electrons having a preferred magnetic-moment spin has a rotatory-type response that is gyrotropic. In contrast, when the helicity is chosen as the spin operator, the response of an electron gas with a preferred helicity spin has a rotatory response that is analogous to an optically active medium. The distinction between these spin operators does not appear in conventional treatments of spin-dependence in quantum plasmas.
ISSN:2331-8422
DOI:10.48550/arxiv.2104.00565