2012/09/30 by Koichi Hattori, Kazunori Itakura
Computer Science · Physics and Astronomy · #Landau quantization #Magnetic field #Photon #Photon polarization #Polarization (electrochemistry) #Quantum Information and Cryptography #Quantum and Classical Electrodynamics #Quantum optics and atomic interactions #Tensor (intrinsic definition) #Vacuum polarization #astro-ph.HE #hep-ph #hep-th #nucl-th
paper · pdf · doi:10.1016/j.aop.2012.11.010
published as Ann. Phys. 330 (2013) 23-54 · To appear in Ann. Phys., 47 pages, 7 figures
openalex publication_date 2012/11/30 · arxiv created 2012/12/06 · arxiv updated 2013/05/02 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
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.