Vacuum Birefringence in a Supercritical Magnetic Field
Keywords:vacuum birefringence, quantum field theory, strong magnetic field
The birefringence effect in vacuum in strong magnetic fields has been considered. The polarization tensor in a constant external magnetic field is analyzed in the framework of quantum field theory and on the basis of the electron Green’s function calculated as the sum over the Landau levels. The case of the lowest Landau levels for photons with the energies below the electron-positron pair creation threshold is considered, and the corresponding refractive indices of the physical vacuum for anomalous and normal waves are determined.
E. Zavattini, G. Zavattini, G. Ruoso, G. Raiteri, E. Polacco, E. Milotti, V. Lozza, M. Karuza, U. Gastaldi, G. Di Domenico, F. Della Valle, R. Cimino, S. Carusotto, G. Cantatore, M. Bregant. New PVLAS results and limits on magnetically induced optical rotation and ellipticity in vacuum. Phys. Rev. D 77, 032006 (2008). https://doi.org/10.1103/PhysRevD.77.032006
F. Della Valle, E. Milotti, A. Ejlli, G. Piemontese, G. Zavattini, U. Gastaldi, R. Pengo, G. Ruoso. First results from the new PVLAS apparatus: A new limit on vacuum magnetic birefringence. Phys. Rev. D 90, 092003 (2014). https://doi.org/10.1103/PhysRevD.90.092003
F. Della Valle, A. Ejlli, U. Gastaldi, G. Messineo, E. Milotti, R. Pengo, G. Ruoso, G. Zavattini. The PVLAS experiment: measuring vacuum magnetic birefringence and dichroism with a birefringent Fabry–Perot cavity. Eur. Phys. J. C 76, 24 (2016). https://doi.org/10.1140/epjc/s10052-015-3869-8
A. Di. Piazza, C. Muller, K.Z. Hatsagortsyan, C.H. Keitel. Extremely high-intensity laser interactions with fundamental quantum systems. Rev. Mod. Phys. 84, 1177 (2012). https://doi.org/10.1103/RevModPhys.84.1177
J.P. Zou, C. Le Blanc, D.N. Papadopoulos, G. Cheriaux, P. Georges, G. Mennerat, F. Druon, L. Lecherbourg, A. Pellegrina, P. Ramirez et al. Design and current progress of the Apollon 10 PW project. High Power Laser Sci. Eng. 3, e2 (2015). https://doi.org/10.1017/hpl.2014.41
H.P. Schlenvoigt, T. Heinzl, U. Schramm, T. Cowan, R. Sauerbrey. Prospects for studying vacuum polarisation using dipole and synchrotron radiation. Phys. Scr. 91, 023010 (2016). https://doi.org/10.1088/0031-8949/91/2/023010
O. Tesileanu, D. Ursescu, R. Dabu, N.V. Zamfir. Extreme light infrastructure. J. Phys.: Conf. Ser. 420, 012157 (2013). https://doi.org/10.1088/1742-6596/420/1/012157
R.P. Mignani, V. Testa, D. Gonzalez Caniulef, R. Taverna, R. Turolla, S. Zane, K. Wu. Evidence for vacuum birefringence from the first optical-polarimetry measurement of the isolated neutron star RX J1856.5–3754. Mon. Not. R. Astron. Soc. 465, 492 (2017). https://doi.org/10.1093/mnras/stw2798
H. Euler, B. Kockel, The scattering of light by light in the Dirac theory. Naturwissenschaften 23, 246 (1935). https://doi.org/10.1007/BF01493898
W. Heisenberg, H. Euler. Folgerungen aus der Diracschen Theorie des Positrons. Z. Phys. 98, 714 (1936). https://doi.org/10.1007/BF01343663
I.A. Batalin, A.E. Shabad. Green's function of a photon in a constant homogeneous electromagnetic field of general form. JETP 33, 483 (1971).
J. Schwinger. On gauge invariance and vacuum polarization. Phys. Rev. 82, 664 (1951). https://doi.org/10.1103/PhysRev.82.664
S. Adler. Photon splitting and photon dispersion in a strong magnetic field. Ann. Phys. 67, 599 (1971). https://doi.org/10.1016/0003-4916(71)90154-0
W. Tsai. Vacuum polarization in homogeneous magnetic fields. Phys. Rev. D 10, 2699 (1974). https://doi.org/10.1103/PhysRevD.10.2699
V.M. Katkov. Polarization operator of a photon in a magnetic field. Zh. ` Eksp. Teor. Fiz. 150, 229 (2016) (in Russian).
W. Tsai, T. Erber. Propagation of photons in homogeneous magnetic fields: Index of refraction. Phys. Rev. D 15, 1132 (1975). https://doi.org/10.1103/PhysRevD.12.1132
K. Kohri, S. Yamada. Polarization tensors in strong magnetic fields. Phys. Rev. D 65, 043006 (2002). https://doi.org/10.1103/PhysRevD.65.043006
A. Shabad. Photon dispersion in a strong magnetic field. Ann. Phys. 90, 166 (1975). https://doi.org/10.1016/0003-4916(75)90144-X
M. Diachenko, O. Novak, R. Kholodov. A cascade of e?e+ pair production by a photon with subsequent annihilation to a single photon in a strong magnetic field. Laser Phys. 26, 066001 (2016). https://doi.org/10.1088/1054-660X/26/6/066001
K. Hattori, K. Itakura. Vacuum birefringence in strong magnetic fields: (I) Photon polarization tensor with all the Landau levels. Ann. Phys. 330, 23 (2013). https://doi.org/10.1016/j.aop.2012.11.010
K. Hattori, K. Itakura. Vacuum birefringence in strong magnetic fields: (II) Complex refractive index from the lowest Landau level. Ann. Phys. 334, 58 (2013). https://doi.org/10.1016/j.aop.2013.03.016
G. Calucci, R. Ragazzon. Nonlogarithmic terms in the strong field dependence of the photon propagator. J. Phys. A 27, 2161 (1994). https://doi.org/10.1088/0305-4470/27/6/036
V.P. Gusynin, V.A. Miransky, I.A. Shovkovy. Dimensional reduction and catalysis of dynamical symmetry breaking by a magnetic field. Nucl. Phys. B 462, 249 (1996). https://doi.org/10.1016/0550-3213(96)00021-1
A. Chodos, K. Everding, D.A. Owen. QED with a chemical potential: The case of a constant magnetic field. Phys. Rev. D 42, 2881 (1990). https://doi.org/10.1103/PhysRevD.42.2881
V.P. Gusynin, V.A. Miransky, I.A. Shovkovy. Dynamical chiral symmetry breaking by a magnetic field in QED. Phys. Rev. D 52, 4747 (1995). https://doi.org/10.1103/PhysRevD.52.4747
V.P. Gusynin, V.A. Miransky, I.A. Shovkovy. Dimensional reduction and dynamical chiral symmetry breaking by a magnetic field in 3 + 1 dimensions. Phys. Lett. B 349, 477 (1995). https://doi.org/10.1016/0370-2693(95)00232-A
D.B. Melrose, A.J. Parle. Quantum electrodynamics in strong magnetic fields. I. Electron states. Aust. J. Phys. 36, 755 (1983). https://doi.org/10.1071/PH830755
P.I. Fomin, R.I. Kholodov. To the theory of resonance quantum electrodynamic processes in an external magnetic field. Ukr. Fiz. Zh. 44, 1526 (1999) (in Ukrainian).
M.M. Dyachenko, O.P. Novak, R.I. Kholodov. Resonant threshold two-photon e?e+ pair production onto the lowest Landau levels in a strong magnetic field. Ukr. J. Phys. 59, 849 (2014). https://doi.org/10.15407/ujpe59.09.0849
M.M. Diachenko, O.P. Novak, R.I. Kholodov. Pair production in a magnetic and radiation field in a pulsar magnetosphere. Mod. Phys. Lett. A 30, 1550111 (2015). https://doi.org/10.1142/S0217732315501114
M.M. Diachenko, O.P. Novak, R.I. Kholodov. Resonant generation of an electron–positron pair by two photons to excited Landau levels. JETP 121, 813 (2015). https://doi.org/10.1134/S1063776115110126
N.N. Bogoliubov, D.V. Shirkov. Introduction to the Theory of Quantized Field (Interscience Publishers, 1959).
K. Fukushima. Magnetic-field induced screening effect and collective excitations. Phys. Rev. D 83, 111501 (2011). https://doi.org/10.1103/PhysRevD.83.111501
A.E. Shabad. Interaction of electromagnetic radiation with supercritical magnetic field. In Workshop SMFNS/ICIMAF, Havana (2004), p. 0307214.
A.A. Sokolov, I.M. Ternov, V.G. Bagrov, R.A. Rzayev. Synchrotron Radiation (Nauka, 1966) (in Russian).
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