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

TL;DR

This paper investigates how the choice of spin operator influences the form of the response tensor in a spin-dependent electron gas, revealing different gyrotropic and optical activity responses.

Contribution

It introduces a covariant response tensor framework for a magnetic-moment polarized electron gas and compares effects of different spin operator choices.

Findings

Magnetic-moment spin yields a gyrotropic response.

Helicity spin results in an optically active-like response.

The choice of spin operator affects the response tensor form.

Abstract

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.