Vacuum birefringence in strong magnetic fields: (I) Photon polarization tensor with all the Landau levels
- Theory Center, IPNS, High Energy Accelerator Research Organization (KEK), 1-1 Oho, Tsukuba, Ibaraki 305-0801 (Japan)
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. - Highlights: Black-Right-Pointing-Pointer Vacuum birefringence is studied in the presence of externally applied magnetic field. Black-Right-Pointing-Pointer A general framework is given on the basis of a vacuum polarization tensor of photon. Black-Right-Pointing-Pointer A resummed vacuum polarization tensor is calculated analytically and exactly. Black-Right-Pointing-Pointer Contributions of all the Landau levels are obtained in the form of an infinite sum. Black-Right-Pointing-Pointer Threshold behavior of real-photon decay is obtained at the each Landau level.
- OSTI ID:
- 22157077
- Journal Information:
- Annals of Physics (New York), Vol. 330; Other Information: Copyright (c) 2012 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA); ISSN 0003-4916
- Country of Publication:
- United States
- Language:
- English
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