We discuss the gauge parameter dependence of particle spectra in statistical quantum electrodynamics and conclude that the electron spectrum is gaugeparameter dependent. The physical spectrum being obtained in the Landau gauge, which leads to gauge invariance in a restricted class of gauge transformations. We compute the thermal self-energy of electrons in a dense media to first order in the fine structure constant. In the zero-temperature limit and at high density the dispersion equation is solved for some gauges, the curves differing from that corresponding to the physical transverse gauge.
We compute the dispersion curves for neutrinos propagating in a very dense electroweak plasma, in magnetic fields of order [Formula: see text]. The neutrino self-energy is calculated in the one-loop approximation. The dispersion equation is solved for motion parallel and perpendicular to the external magnetic field. We obtain an effective neutrino mass which increases with the magnetic field, up to values B where threshold energy for creation of W± pairs (out from the thermal background) is reached.
The 2D screening is investigated in a simple single band square tight-binding model which qualitatively resembles the known electronic structure in high temperature superconductors. The Coulomb kernel for the two particle Bethe-Salpeter equation in the single loop (RPA) approximation for the polarization can be evaluated in a strong tight binding limit. The results indicate an intense screening of the Coulomb repulsion between the particles, which becomes stronger and anisotropic when the Fermi level approach half filling (or equivalently, when the Fermi surface approach the Van Hove singularities) and rapidly decreases away it. The effect is also more pronounced for quasi-momenta regions near the corners of the Brillouin cell, which correspond to dual spatial distances of the order few unit cells. Therefore, a possible mechanism is identified which could explain the existence of extremely small Cooper pairs in these materials, as bounded anisotropic composites joined by residual super-exchange or phonon interactions.
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