In-medium polarization tensor in strong magnetic fields (I): Magneto-birefringence at finite temperature and density

TL;DR

This paper analyzes the in-medium polarization tensor of fermion pairs in strong magnetic fields at finite temperature and density, revealing detailed real and imaginary parts and their implications for photon dispersion and magneto-birefringence.

Contribution

It provides a comprehensive analytic form of the polarization tensor at zero temperature and finite density, highlighting cancellation effects and threshold behavior modifications.

Findings

Complete analytic form of polarization tensor at zero temperature and finite density.

Identification of threshold behavior shifts due to medium effects.

Demonstration of polarization-dependent photon dispersion (magneto-birefringence).

Abstract

We investigate in-medium polarization effects of the fermion and antifermion pairs at finite temperature and density in strong magnetic fields within the lowest Landau level approximation. Inspecting the integral representation of the polarization tensor by analytic and numerical methods, we provide both the real and imaginary parts of the polarization tensor obtained after delicate interplay between the vacuum and medium contributions essentially due to the Pauli-blocking effect. Especially, we provide a complete analytic form of the polarization tensor at zero temperature and finite density that exhibits an exact cancellation and associated relocation of the singular threshold behaviors for a single photon decay to a fermion and antifermion pair. As a physical application of the in-medium polarization tensor, we discuss the magneto-birefringence that is polarization-dependent dispersion relations of photons induced by the strong magnetic fields.