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

• Published in: Annals of physics Vol. 334; pp. 58 - 82
• Main Authors: Hattori, Koichi, Itakura, Kazunori
• Format: Journal Article
• Language: English
• Published: New York Elsevier Inc 01.07.2013; Elsevier BV
• Subjects: APPROXIMATIONS; Atoms & subatomic particles; BIREFRINGENCE; Complex refractive index; ENERGY DEPENDENCE; Lowest Landau level; MAGNETIC FIELDS; Mathematical analysis; PARTICLE DECAY; Photons; Physics; PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; POLARIZATION; Propagation; Real-photon decay; REFRACTIVE INDEX; Refractivity; Strong magnetic field; TENSORS; Vacuum birefringence; VACUUM POLARIZATION; Complex refractive index; Lowest Landau level; Strong magnetic field; Vacuum birefringence; Real-photon decay
• ISSN: 0003-4916; 1096-035X
• DOI: 10.1016/j.aop.2013.03.016

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. •Vacuum birefringence and photon decay are described by the complex refractive index.•Resummed photon vacuum polarization tensor in the lowest Landau level is used.•Back reactions from the distorted Dirac sea are self-consistently taken into account.•Self-consistent treatment drastically changes structure in photon energy dependence.•Dependences on photon propagation angle and magnetic-field strength are presented.