Abstract
We develop covariant chiral kinetic theory with Landau level basis. We use it to investigate a magnetized plasma with a transverse electric field and a steady vorticity as perturbations. After taking into account vacuum shift in the latter case, we find the resulting current and stress tensor in both cases can be matched consistently with constitutive equations of magnetohydrodynamics. We find the solution in the vorticity case contains both shifts in temperature and chemical potential as well as excitations of the lowest Landau level states. The solution gives rise to an vector charge density and axial current density. The vacuum parts coming from both shifts and excitations agree with previous studies and the medium parts coming entirely from excitations leads to a new contribution to vector charge and axial current density consistent with standard chiral vortical effect.
Highlights
Chemical potential sgn(qf )B · ω for particle
We develop covariant chiral kinetic theory with Landau level basis
The vacuum parts coming from both shifts and excitations agree with previous studies and the medium parts coming entirely from excitations leads to a new contribution to vector charge and axial current density consistent with standard chiral vortical effect
Summary
We start with a system of right-handed chiral fermions covariantly coupled to external gauge field. Choice is not the most general situation, it allows us to study the magneto-vortical effect in this simple setting It adopts a simple covariant zeroth order solution as [26, 27]. Where μR is the chemical potential for right-handed Weyl fermions. When the magnetic field is not strong enough, summation over Landau levels is needed It is shown in [61] that, in the weak magnetic field limit, the summation jμ will be reduced to the well-known solution proportional to momentum pμ. In the two sections, we will study first order gradient correction to (2.13) induced by constant transverse electric field and vorticity respectively.
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