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

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.

In-medium polarization tensor in strong magnetic fields (II): Axial Ward identity at finite temperature and density

“…In this series of papers, we investigate the polarization effects of the medium particles at finite temperature and/or density as well as of the vacuum fluctuations in strong magnetic fields. In the first paper [1], which is referred to as Paper I, we have provided the explicit forms of the vacuum and medium contributions to the one-loop polarization tensor in the lowest Landau level (LLL) approximation and discussed magneto-birefringence as a physical application, that is, the polarization-dependent photon dispersion relation induced by the strong magnetic fields. We have inspected delicate interplay between the vacuum and medium contributions.…”

“…The whole non-conservation equation of the axial-vector current, which we call the axial Ward identity (AWI), is controlled by the balance between the anomalous and mass-dependent terms that arise from the divergent and finite pieces of the loop integral. 1 Since the mass-dependent part in the AWI is not anomalous in nature, it does not exhibit simple behaviors in general when one varies magnitudes of relevant parameters such as the external photon momenta, fermion mass, temperature and/or density. Therefore, the AWI as a whole is not simply governed by the anomalous term and, moreover, the two terms can be comparable in magnitude, implying that the axial-vector current could be effectively conserved in some parameter regimes.…”