Vacuum birefringence in strong magnetic fields: (I) Photon polarization tensor with all the Landau levels

• Published in: Annals of physics Vol. 330; pp. 23 - 54
• Main Authors: Hattori, Koichi, Itakura, Kazunori
• Format: Journal Article
• Language: English
• Published: New York Elsevier Inc 01.03.2013; Elsevier BV
• Subjects: Approximation; APPROXIMATIONS; Atoms & subatomic particles; BIREFRINGENCE; ENERGY LEVELS; FERMIONS; INTEGRALS; Landau level; MAGNETIC FIELDS; Mathematical analysis; Mathematical models; PARTICLE DECAY; PHOTONS; Physics; PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; POLARIZATION; REFRACTIVE INDEX; Refractivity; Strong magnetic field; TENSORS; Vacuum birefringence; VACUUM POLARIZATION; Vacuum birefringence; Landau level; Strong magnetic field
• ISSN: 0003-4916; 1096-035X
• DOI: 10.1016/j.aop.2012.11.010

Photons propagating in strong magnetic fields are subject to a phenomenon called the “vacuum birefringence” where refractive indices of two physical modes both deviate from unity and are different from each other. We compute the vacuum polarization tensor of a photon in a static and homogeneous magnetic field by utilizing Schwinger’s proper-time method, and obtain a series representation as a result of double integrals analytically performed with respect to proper-time variables. The outcome is expressed in terms of an infinite sum of known functions which is plausibly interpreted as summation over all the Landau levels of fermions. Each contribution from infinitely many Landau levels yields a kinematical condition above which the contribution has an imaginary part. This indicates decay of a sufficiently energetic photon into a fermion–antifermion pair with corresponding Landau level indices. Since we do not resort to any approximation, our result is applicable to the calculation of refractive indices in the whole kinematical region of a photon momentum and in any magnitude of the external magnetic field. ► Vacuum birefringence is studied in the presence of externally applied magnetic field. ► A general framework is given on the basis of a vacuum polarization tensor of photon. ► A resummed vacuum polarization tensor is calculated analytically and exactly. ► Contributions of all the Landau levels are obtained in the form of an infinite sum. ► Threshold behavior of real-photon decay is obtained at the each Landau level.