Thermal fermionic dispersion relations in a magnetic field

Abstract

The thermal self-energy of an electron in a static uniform magnetic field B is calculated to first order in the fine structure constant α and to all orders in eB. We use two methods, one based on the Furry picture and another based on Schwinger's proper-time method. As external states we consider relativistic Landau levels with special emphasis on the lowest Landau level. In the high-temperature limit we derive self-consistent dispersion relations for particle and hole excitations, showing the chiral asymmetry caused by the external field. For weak fields, earlier results on the groundstate energy and the anomalous magnetic moment are discussed and compared with the present analysis. In the strong-field limit the appearance of a field-independent imaginary part of the self-energy, related to Landau damping in the e + e − plasma, is pointed out.

Neutrino self-energy and dispersion in a medium with a magnetic field

“…and obtain the following expression [2,6] of the propagator S(x ′ , x ′′ ) in the presence of an external magnetic field and a plasma at non-zero temperature and density,…”

Neutrino dispersion in magnetized media and spin oscillations in the early Universe

“…(4) and (5). For the non-local neutrino self-energy term it is convenient to start from the electron propagator in the Schwinger proper-time form, which can be written as [19,21]:…”

Gauge independence and relativistic dispersion equations in statistical QED

“…Thus, from (12) or (14) it is seen that the poles of the electron Green function become independent of the unphysical photon modes if it is taken the limit α → ∞ words, by eliminating the contribution of these modes to Σ. The zero temperature QED case can be treated by following similar arguments.…”

“…Note that we get two different dispersion relations for particles and holes, unlike other results at finite temperature, such as densities near the electron mass [17], high temperature but without chemical potential [10], and others [18]. By taking into account the electron mass, we correct the pathological behavior of the derivative of the dispersion curve at p = 0 obtained by several authors for massless fermions [11,19,1,12,20].…”

“…For finite temperature, this invariance has been also formally shown [9]. In the literature it has been explicitly verified this conclusion in several limiting cases [10][11][12]. However, it should be noted that the calculation of the mass operator is carried out precisely to investigate the system perturbatively out of the mass shell , where the condition of gauge parameter independence frequently mentioned (see i.e.…”