Improved ring potential of QED at finite temperature and in the presence of weak and strong magnetic fields

Abstract

Using the general structure of the vacuum polarization tensor Π µν (k 0 , k) in the infrared (IR) limit, k 0 → 0, the ring contribution to QED effective potential at finite temperature and non-zero magnetic field is determined beyond the static limit, (k 0 → 0, k → 0). The resulting ring potential is then studied in weak and strong magnetic field limit. In the limit of weak magnetic field, at high temperature and for α → 0, the improved ring potential consists of a term proportional to T 4 α 5/2 , in addition to the expected T 4 α 3/2 term arising from the static limit. Here, α is the fine structure constant. In the limit of strong magnetic field, where QED dynamics is dominated by the lowest Landau level (LLL), the ring potential includes a novel term consisting of dilogarithmic function (eB)Li 2 − 2α π eB m 2 . Using the ring improved (one-loop) effective potential including the one-loop effective potential and ring potential in the IR limit, the dynamical chiral symmetry breaking of QED is studied at finite temperature and in the presence of strong magnetic field. The gap equation, the dynamical mass and the critical temperature of QED in the regime of LLL dominance are determined in the improved IR as well as in the static limit. For a given value of magnetic field, the improved ring potential is shown to be more efficient in decreasing the critical temperature arising from one-loop effective potential.

Chiral magnetic conductivity

“…In this case there are resonances at ω = 5µ 5 and ω = µ 5 . Equation (45) shows that the imaginary part is proportional to ω 2 , therefore the second resonance at ω = 5µ 5 is much stronger than the first one at ω = µ 5 . Because the second resonance is due to the right-handed modes, and the first one due to left-handed, the contribution of the second resonance has opposite sign to the first resonance.…”

“…Also it would be interesting to study the effects of a time-dependent magnetic field on other physical quantities and effects, like for example the chiral condensate, the chiral phase transition and dynamical chiral symmetry breaking. So far these have only been investigated in a constant magnetic field [41,42,43,44,45,46,47].…”

Local electric current correlation function in an exponentially decaying magnetic field

“…In this section, we will compare the values of ψ ψ c LLL from (III.6) with ψ ψ LLL from (III.14), as well as χ (i) 0 from (IV.13) with χ (i) LLL from (IV.24), in order to explore the effect of inhomogeneity of the external magnetic field, especially once quantum corrections are taken into account. To do this, let us first 7 We are working in the units where eB = 1 GeV 2 corresponds to B 0 ∼ 1.7 × 10 20 Gauß [25]. 8 As it turns out, the magnetic length ℓ B for eB 0 = 1 GeV 2 is given by ℓ B ∼ 0.63 fm.…”

Symmetry restoration at finite temperature with weak magnetic fields

“…(24). This means that in general, these self-energies can be written as linear combinations of nine independent structures [43,44]. Since we are interested in considering the infrared limit, q 0 = 0, q → 0, only u µ and b µ remain.…”