The QED effective action at finite temperature and density is calculated to all orders in an external homogeneous and time-independent magnetic field in the weak coupling limit. The free energy, obtained explicitly, exhibit the expected de Haas -van Alphen oscillations. An effective coupling at finite temperature and density is derived in a closed form and is compared with renormalization group results.
We derive general expressions for the neutrino dispersion relation in a magnetized plasma with a wide range of temperatures, chemical potentials, and magnetic field strengths. If the electron and proton chemical potentials vanish, as in the early Universe, there is no magnetization contribution to the neutrino refractive index to leading order in the Fermi coupling constant, contrary to claims in the recent literature. Therefore, as long as the magnetic field satisfies B < ∼ T 2 , the neutrino refractive index in the early Universe is dominated by the standard "non-local term". If neutrinos are Dirac particles with magnetic moment µ, then their right-handed components are thermally populated before the nucleosynthesis epoch by magnetically induced spin oscillations if µB 0 > ∼ 10 −6 µ B gauss, where µ B = e/2m e is the Bohr magneton and B 0 is a large-scale primordial magnetic field at T 0 ≈ 1 MeV. For a typically expected random field distribution, even smaller values for µB 0 would suffice to thermalize the right-handed Dirac components.
The one-loop effective action for a slowly varying electromagnetic field is computed at finite temperature and density using a real-time formalism.We discuss the gauge invariance of the result. Corrections to the Debye mass from an electric field are computed at high temperature and high density. The effective coupling constant, defined from a purely electric weak-field expansion, behaves at high temperature very differently from the case of a magnetic field, and does not satisfy the renormalization group equation. The issue of pair production in the real-time formalism is discussed and also its relevance for heavy-ion collisions. 1
The thermal averaged real-time propagator of a Dirac fermion in a static uniform magnetic field B is derived. At non-zero chemical potential and temperature we find explicitly the effective action for the magnetic field, which is shown to be closely related to the Helmholz free energy of a relativistic fermion gas, and it exhibits the expected de Haas -van Alphen oscillations. An effective QED coupling constant at finite temperature and density is derived, and compared with renormalization group results. We discuss some astrophysical implications of our results.
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