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Euler–Heisenberg Lagrangian

November 23, 2023

In physics, the Euler–Heisenberg Lagrangian describes the non-linear dynamics of electromagnetic fields in vacuum. It was first obtained by Werner Heisenberg and Hans Heinrich Euler[1] in 1936. By treating the vacuum as a medium, it predicts rates of quantum electrodynamics (QED) light interaction processes.[clarification needed]

Physics edit

It takes into account vacuum polarization to one loop, and is valid for electromagnetic fields that change slowly compared to the inverse electron mass,

 

Here m is the electron mass, e the electron charge,  , and  .

In the weak field limit, this becomes

 

It describes photon–photon scattering in QED; Robert Karplus and Maurice Neuman calculated the full amplitude,[2] which is very small.

Experiments edit

Delbrück scattering of gamma rays was observed in 1953 by Robert Wilson.[3] Photon splitting in strong magnetic fields was measured in 2002.[4] Light-by-light scattering can be studied using the strong electromagnetic fields of the hadrons collided at the LHC,[5][6] and its observation was reported by the ATLAS Collaboration in 2019.[7]

PVLAS is searching for vacuum polarization of laser beams crossing magnetic fields to detect effects from axion dark matter. No signal has been found and searches continue. OSQAR at CERN is also studying vacuum birefringence.

In 2016 a team of astronomers from Italy, Poland, and the U.K. reported[8][9] observations of the light emitted by a neutron star (pulsar RX J1856.5−3754). The star is surrounded by a very strong magnetic field (1013 G), and birefringence is expected from the vacuum polarization described by the Euler–Heisenberg Lagrangian. A degree of polarization of about 16% was measured and was claimed to be "large enough to support the presence of vacuum birefringence, as predicted by QED". Fan et al. pointed that their results are uncertain due to low accuracy of star model and the direction of the neutron magnetization axis.[10]

In July 2021 the first known observation of vacuum birefringence was reported by the STAR experiment at the Relativistic Heavy Ion Collider, the Breit–Wheeler process was also studied although only evidence was reported[11][12][13]

In May 2022 the first study of IXPE has hinted the possibility of vacuum birefringence on 4U 0142+61.[14][15]

See also edit

References edit

  1. ^ Heisenberg, W.; Euler, H. (1936). "Folgerungen aus der Diracschen Theorie des Positrons". Zeitschrift für Physik (in German). 98 (11–12): 714–732. Bibcode:1936ZPhy...98..714H. doi:10.1007/bf01343663. ISSN 1434-6001.
  2. ^ Karplus, Robert; Neuman, Maurice (1951-08-15). "The Scattering of Light by Light". Physical Review. 83 (4): 776–784. Bibcode:1951PhRv...83..776K. doi:10.1103/physrev.83.776. ISSN 0031-899X.
  3. ^ Akhmadaliev, Sh. Zh.; Kezerashvili, G. Ya.; Klimenko, S. G.; Malyshev, V. M.; Maslennikov, A. L.; et al. (1998-11-01). "Delbrück scattering at energies of 140–450 MeV". Physical Review C. 58 (5): 2844–2850. arXiv:hep-ex/9806037. Bibcode:1998PhRvC..58.2844A. doi:10.1103/physrevc.58.2844. ISSN 0556-2813. S2CID 118059928.
  4. ^ Akhmadaliev, Sh. Zh.; Kezerashvili, G. Ya.; Klimenko, S. G.; Lee, R. N.; Malyshev, V. M.; et al. (2002-07-19). "Experimental Investigation of High-Energy Photon Splitting in Atomic Fields". Physical Review Letters. 89 (6): 061802. arXiv:hep-ex/0111084. Bibcode:2002PhRvL..89f1802A. doi:10.1103/physrevlett.89.061802. ISSN 0031-9007. PMID 12190576. S2CID 18759344.
  5. ^ d’Enterria, David; da Silveira, Gustavo G. (22 August 2013). "Observing Light-by-Light Scattering at the Large Hadron Collider". Physical Review Letters. American Physical Society (APS). 111 (8): 080405. arXiv:1305.7142. Bibcode:2013PhRvL.111h0405D. doi:10.1103/physrevlett.111.080405. ISSN 0031-9007. PMID 24010419. S2CID 43797550.
  6. ^ Michael Schirber (22 Aug 2013). "Synopsis: Spotlight on Photon-Photon Scattering". Physical Review Letters. 111 (8): 080405. arXiv:1305.7142. Bibcode:2013PhRvL.111h0405D. doi:10.1103/PhysRevLett.111.080405. PMID 24010419. S2CID 43797550.
  7. ^ "ATLAS observes light scattering off light". 2019-03-17.
  8. ^ Mignani, R. P.; Testa, V.; González Caniulef, D.; Taverna, R.; Turolla, R.; Zane, S.; Wu, K. (2016-11-02). "Evidence for vacuum birefringence from the first optical-polarimetry measurement of the isolated neutron star RX J1856.5−3754". Monthly Notices of the Royal Astronomical Society. 465 (1): 492–500. arXiv:1610.08323. doi:10.1093/mnras/stw2798. ISSN 0035-8711.
  9. ^ "Astronomers Report First Observational Evidence for Vacuum Birefringence | Astronomy | Sci-News.com". Breaking Science News | Sci-News.com. Retrieved 2021-10-10.
  10. ^ Fan, Xing; Kamioka, Shusei; Inada, Toshiaki; Yamazaki, Takayuki; Namba, Toshio; et al. (2017). "The OVAL experiment: a new experiment to measure vacuum magnetic birefringence using high repetition pulsed magnets". The European Physical Journal D. 71 (11): 308. arXiv:1705.00495. Bibcode:2017EPJD...71..308F. doi:10.1140/epjd/e2017-80290-7. ISSN 1434-6060. S2CID 119476135.
  11. ^ STAR Collaboration; Adam, J.; Adamczyk, L.; Adams, J. R.; Adkins, J. K.; Agakishiev, G.; Aggarwal, M. M.; Ahammed, Z.; Alekseev, I.; Anderson, D. M.; Aparin, A. (2021-07-27). "Measurement of e+e− Momentum and Angular Distributions from Linearly Polarized Photon Collisions". Physical Review Letters. 127 (5): 052302. arXiv:1910.12400. Bibcode:2021PhRvL.127e2302A. doi:10.1103/PhysRevLett.127.052302. PMID 34397228. S2CID 236906272.
  12. ^ "Collisions of Light Produce Matter/Antimatter from Pure Energy". Brookhaven National Laboratory. Retrieved 2021-10-10.
  13. ^ "Colliding photons were spotted making matter. But are the photons 'real'?". Science News. 2021-08-09. Retrieved 2021-09-02.
  14. ^ Taverna, Roberto; Turolla, Roberto; Muleri, Fabio; Heyl, Jeremy; Zane, Silvia; Baldini, Luca; Caniulef, Denis González; Bachetti, Matteo; Rankin, John; Caiazzo, Ilaria; Di Lalla, Niccolò; Doroshenko, Victor; Errando, Manel; Gau, Ephraim; Kırmızıbayrak, Demet (2022-05-18). "Polarized x-rays from a magnetar". Science. 378 (6620): 646–650. arXiv:2205.08898. Bibcode:2022Sci...378..646T. doi:10.1126/science.add0080. PMID 36356124. S2CID 248863030.
  15. ^ "X-ray polarisation probes extreme physics". CERN Courier. 2022-06-30. Retrieved 2022-08-15.

November 23, 2023
euler, heisenberg, lagrangian, physics, describes, linear, dynamics, electromagnetic, fields, vacuum, first, obtained, werner, heisenberg, hans, heinrich, euler, 1936, treating, vacuum, medium, predicts, rates, quantum, electrodynamics, light, interaction, pro. In physics the Euler Heisenberg Lagrangian describes the non linear dynamics of electromagnetic fields in vacuum It was first obtained by Werner Heisenberg and Hans Heinrich Euler 1 in 1936 By treating the vacuum as a medium it predicts rates of quantum electrodynamics QED light interaction processes clarification needed Contents 1 Physics 2 Experiments 3 See also 4 ReferencesPhysics editIt takes into account vacuum polarization to one loop and is valid for electromagnetic fields that change slowly compared to the inverse electron mass L F 1 8 p 2 0 exp m 2 s e s 2 Re cosh e s 2 F i G Im cosh e s 2 F i G G 2 3 e s 2 F 1 d s s 3 displaystyle mathcal L mathcal F frac 1 8 pi 2 int 0 infty exp left m 2 s right left es 2 frac operatorname Re cosh left es sqrt 2 left mathcal F i mathcal G right right operatorname Im cosh left es sqrt 2 left mathcal F i mathcal G right right mathcal G frac 2 3 es 2 mathcal F 1 right frac ds s 3 nbsp Here m is the electron mass e the electron charge F 1 2 B 2 E 2 displaystyle mathcal F frac 1 2 left mathbf B 2 mathbf E 2 right nbsp and G E B displaystyle mathcal G mathbf E cdot mathbf B nbsp In the weak field limit this becomes L 1 2 E 2 B 2 2 a 2 45 m 4 E 2 B 2 2 7 E B 2 displaystyle mathcal L frac 1 2 left mathbf E 2 mathbf B 2 right frac 2 alpha 2 45m 4 left left mathbf E 2 mathbf B 2 right 2 7 left mathbf E cdot mathbf B right 2 right nbsp It describes photon photon scattering in QED Robert Karplus and Maurice Neuman calculated the full amplitude 2 which is very small Experiments editDelbruck scattering of gamma rays was observed in 1953 by Robert Wilson 3 Photon splitting in strong magnetic fields was measured in 2002 4 Light by light scattering can be studied using the strong electromagnetic fields of the hadrons collided at the LHC 5 6 and its observation was reported by the ATLAS Collaboration in 2019 7 PVLAS is searching for vacuum polarization of laser beams crossing magnetic fields to detect effects from axion dark matter No signal has been found and searches continue OSQAR at CERN is also studying vacuum birefringence In 2016 a team of astronomers from Italy Poland and the U K reported 8 9 observations of the light emitted by a neutron star pulsar RX J1856 5 3754 The star is surrounded by a very strong magnetic field 1013 G and birefringence is expected from the vacuum polarization described by the Euler Heisenberg Lagrangian A degree of polarization of about 16 was measured and was claimed to be large enough to support the presence of vacuum birefringence as predicted by QED Fan et al pointed that their results are uncertain due to low accuracy of star model and the direction of the neutron magnetization axis 10 In July 2021 the first known observation of vacuum birefringence was reported by the STAR experiment at the Relativistic Heavy Ion Collider the Breit Wheeler process was also studied although only evidence was reported 11 12 13 In May 2022 the first study of IXPE has hinted the possibility of vacuum birefringence on 4U 0142 61 14 15 See also editBirefringence Circular dichroism Chiral magnetic effect Schwinger limit Schwinger effect Uehling potential Electric polarization Kerr effectReferences edit Heisenberg W Euler H 1936 Folgerungen aus der Diracschen Theorie des Positrons Zeitschrift fur Physik in German 98 11 12 714 732 Bibcode 1936ZPhy 98 714H doi 10 1007 bf01343663 ISSN 1434 6001 Karplus Robert Neuman Maurice 1951 08 15 The Scattering of Light by Light Physical Review 83 4 776 784 Bibcode 1951PhRv 83 776K doi 10 1103 physrev 83 776 ISSN 0031 899X Akhmadaliev Sh Zh Kezerashvili G Ya Klimenko S G Malyshev V M Maslennikov A L et al 1998 11 01 Delbruck scattering at energies of 140 450 MeV Physical Review C 58 5 2844 2850 arXiv hep ex 9806037 Bibcode 1998PhRvC 58 2844A doi 10 1103 physrevc 58 2844 ISSN 0556 2813 S2CID 118059928 Akhmadaliev Sh Zh Kezerashvili G Ya Klimenko S G Lee R N Malyshev V M et al 2002 07 19 Experimental Investigation of High Energy Photon Splitting in Atomic Fields Physical Review Letters 89 6 061802 arXiv hep ex 0111084 Bibcode 2002PhRvL 89f1802A doi 10 1103 physrevlett 89 061802 ISSN 0031 9007 PMID 12190576 S2CID 18759344 d Enterria David da Silveira Gustavo G 22 August 2013 Observing Light by Light Scattering at the Large Hadron Collider Physical Review Letters American Physical Society APS 111 8 080405 arXiv 1305 7142 Bibcode 2013PhRvL 111h0405D doi 10 1103 physrevlett 111 080405 ISSN 0031 9007 PMID 24010419 S2CID 43797550 Michael Schirber 22 Aug 2013 Synopsis Spotlight on Photon Photon Scattering Physical Review Letters 111 8 080405 arXiv 1305 7142 Bibcode 2013PhRvL 111h0405D doi 10 1103 PhysRevLett 111 080405 PMID 24010419 S2CID 43797550 ATLAS observes light scattering off light 2019 03 17 Mignani R P Testa V Gonzalez Caniulef D Taverna R Turolla R Zane S Wu K 2016 11 02 Evidence for vacuum birefringence from the first optical polarimetry measurement of the isolated neutron star RX J1856 5 3754 Monthly Notices of the Royal Astronomical Society 465 1 492 500 arXiv 1610 08323 doi 10 1093 mnras stw2798 ISSN 0035 8711 Astronomers Report First Observational Evidence for Vacuum Birefringence Astronomy Sci News com Breaking Science News Sci News com Retrieved 2021 10 10 Fan Xing Kamioka Shusei Inada Toshiaki Yamazaki Takayuki Namba Toshio et al 2017 The OVAL experiment a new experiment to measure vacuum magnetic birefringence using high repetition pulsed magnets The European Physical Journal D 71 11 308 arXiv 1705 00495 Bibcode 2017EPJD 71 308F doi 10 1140 epjd e2017 80290 7 ISSN 1434 6060 S2CID 119476135 STAR Collaboration Adam J Adamczyk L Adams J R Adkins J K Agakishiev G Aggarwal M M Ahammed Z Alekseev I Anderson D M Aparin A 2021 07 27 Measurement of e e Momentum and Angular Distributions from Linearly Polarized Photon Collisions Physical Review Letters 127 5 052302 arXiv 1910 12400 Bibcode 2021PhRvL 127e2302A doi 10 1103 PhysRevLett 127 052302 PMID 34397228 S2CID 236906272 Collisions of Light Produce Matter Antimatter from Pure Energy Brookhaven National Laboratory Retrieved 2021 10 10 Colliding photons were spotted making matter But are the photons real Science News 2021 08 09 Retrieved 2021 09 02 Taverna Roberto Turolla Roberto Muleri Fabio Heyl Jeremy Zane Silvia Baldini Luca Caniulef Denis Gonzalez Bachetti Matteo Rankin John Caiazzo Ilaria Di Lalla Niccolo Doroshenko Victor Errando Manel Gau Ephraim Kirmizibayrak Demet 2022 05 18 Polarized x rays from a magnetar Science 378 6620 646 650 arXiv 2205 08898 Bibcode 2022Sci 378 646T doi 10 1126 science add0080 PMID 36356124 S2CID 248863030 X ray polarisation probes extreme physics CERN Courier 2022 06 30 Retrieved 2022 08 15 Retrieved from https en wikipedia org w index php title Euler Heisenberg Lagrangian amp oldid 1170885588, wikipedia, wiki, book, books, library,

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