Vacuum birefringence in strong magnetic fields: (II) Complex refractive index from the lowest Landau level

TL;DR

This paper calculates the complex refractive index of photons in strong magnetic fields, revealing significant deviations from unity and photon decay phenomena, especially when considering the lowest Landau level approximation.

Contribution

It provides a self-consistent method to compute the complex refractive index of photons in strong magnetic fields, accounting for back reactions and decay processes.

Findings

Refractive index can be very large and complex in strong magnetic fields.

Photon decay into fermion-antifermion pairs occurs at high photon energies.

Self-consistent treatment is essential for accurate refractive index calculations.

Abstract

We compute the refractive indices of a photon propagating in strong magnetic fields on the basis of the analytic representation of the vacuum polarization tensor obtained in our previous paper. When the external magnetic field is strong enough for the fermion one-loop diagram of the polarization tensor to be approximated by the lowest Landau level, the propagating mode in parallel to the magnetic field is subject to modification: The refractive index deviates from unity and can be very large, and when the photon energy is large enough, the refractive index acquires an imaginary part indicating decay of a photon into a fermion-antifermion pair. We study dependences of the refractive index on the propagating angle and the magnetic-field strength. It is also emphasized that a self-consistent treatment of the equation which defines the refractive index is indispensable for accurate description of the refractive index. This self-consistent treatment physically corresponds to consistently including the effects of back reactions of the distorted Dirac sea in response to the incident photon.