The response tensor for a highly relativistic magnetized thermal plasma

The transverse part of the linear response tensor is evaluated for a highly relativistic thermal electron gas, starting from Trubnikov's response tensor for an arbitrary temperature. Three contributions to the response tensor are important. The diagonal components are dominated by an unmagnetized term, which gives the familiar dispersion k(2) = w(p0)(2), where omega(p0) is the proper plasma frequency. The difference between the diagonal components is larger in magnitude than the off-diagonal components, implying that the natural modes are nearly linearly polarized. This leads to a generalized form of Faraday rotation in which linear polarization is partially converted into circular polarization at a rate per unit path length alpha lambda(3) (lambda = wavelength).