Photon polarization tensor in a magnetized plasma system

TL;DR

This paper analyzes the photon polarization tensor in a magnetized plasma at finite temperature, revealing the significance of multiple Landau levels and Landau damping effects, and introduces a convergent method for summation without truncation.

Contribution

It provides a novel, convergent approach to summing Landau levels in the photon polarization tensor at finite temperature, clarifying the limitations of the LLL approximation.

Findings

Landau levels contribute significantly beyond the lowest level at finite temperature.

Landau damping arises from soft field absorption by plasma constituents.

Matsubara frequency summation does not commute with Landau level summation.

Abstract

We investigate the photon polarization tensor at finite temperature in the presence of a static and homogeneous external magnetic field. In our scheme, the Matsubara frequency summation is performed after Poisson summation, which will be taken easily and convergent quickly in the frame of proper time representation. Moreover, the dependence of Landau levels is expressed explicitly. It demonstrates the convergence of summing Landau levels as it has to be. Consequently, there is no necessary to truncate the Landau level in a numerical estimation. At zero temperature, the Lowest Landau Level (LLL) approximation is analytically satisfied for the imaginary parts of the vacuum photon polarization tensor. Our results examine that, the LLL approximation is not enough for the thermal photon polarization tensor, it gains the contribution not only from the lowest Landau level but also up to the finite-$n$ levels. Such large imaginary ones only show up at finite temperatures, which is the so called Landau damping. It originates from the absorption of soft fields by hard plasma constituents, which is a universal feature of plasma systems. Finally, it was argued that the summation of Matsubara frequency is not commuted with Landau level ones, such conjecture is excluded in our calculations.