The fermion self-energy and damping rate in a hot magnetized plasma

Abstract

We derive a general expression for the fermion self-energy in a hot magnetized plasma by using the Landau-level representation. In the one-loop approximation, the Dirac structure of the self-energy is characterized by five different functions that depend on the Landau-level index $n$ and the longitudinal momentum $p_z$. We derive general expressions for all five functions and obtain closed-form expressions for their imaginary parts. The latter receive contributions from three types of on-shell processes, which are interpreted in terms of Landau-level transitions, accompanied by a single photon (gluon) emission or absorption. By making use of the imaginary parts of the self-energy functions, we also derive the Landau-level dependent fermion damping rates ${\Gamma }_n(p_z)$ and study them numerically in a wide range of model parameters. We also demonstrate that the two-spin degeneracy of the Landau levels is lifted by the one-loop self-energy corrections. While the spin splitting of the damping rates is small, it may be important for some spin and chiral effects. We argue that the general method and the numerical results for the rates can have interesting applications in heavy-ion physics, astrophysics, and cosmology, where strongly magnetized QED or QCD plasmas are ubiquitous.

22 pages, 7 multipanel figures; v2: mistakes are corrected; final version accepted for publication in Phys. Rev. D

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• Thermodynamics of strongly magnetized dense quark matter from hard dense loop perturbation theory
• Thermal Field Theory in the Presence of a Background Magnetic Field and its Application to QCD
• Magneto-conductivity and CME in Dirac semimetals from Keldysh technique in Landau levels basis
• Physics of strong electromagnetic fields in relativistic heavy-ion collisions
• Review of heat and charge transport in strongly magnetized relativistic plasmas