Physics:Euler–Heisenberg Lagrangian

From HandWiki
Short description: Effective quantum electrodynamics action

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

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

[math]\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}}. }[/math]

Here m is the electron mass, e the electron charge, [math]\displaystyle{ \mathcal{F}=\frac{1}{2}\left(\mathbf{B}^2 - \mathbf{E}^2\right) }[/math], and [math]\displaystyle{ \mathcal{G}=\mathbf{E}\cdot\mathbf{B} }[/math].

In the weak field limit, this becomes

[math]\displaystyle{ \mathcal{L} = \frac{1}{2}\left(\mathbf{E}^{2}-\mathbf{B}^{2}\right)+\frac{2\alpha^{2}}{45 m^{4}}\left[\left(\mathbf{E}^2 - \mathbf{B}^2\right)^{2} + 7 \left(\mathbf{E}\cdot\mathbf{B}\right)^{2}\right]. }[/math]

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

Experiments

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


References

  1. ↑ Heisenberg, W.; Euler, H. (1936). "Folgerungen aus der Diracschen Theorie des Positrons" (in de). Zeitschrift für Physik 98 (11–12): 714–732. doi:10.1007/bf01343663. ISSN 1434-6001. Bibcode: 1936ZPhy...98..714H. 
  2. ↑ Karplus, Robert; Neuman, Maurice (1951-08-15). "The Scattering of Light by Light". Physical Review 83 (4): 776–784. doi:10.1103/physrev.83.776. ISSN 0031-899X. Bibcode: 1951PhRv...83..776K. 
  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. doi:10.1103/physrevc.58.2844. ISSN 0556-2813. Bibcode: 1998PhRvC..58.2844A. 
  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. doi:10.1103/physrevlett.89.061802. ISSN 0031-9007. PMID 12190576. Bibcode: 2002PhRvL..89f1802A. 
  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. doi:10.1103/physrevlett.111.080405. ISSN 0031-9007. PMID 24010419. Bibcode: 2013PhRvL.111h0405D. 
  6. ↑ Michael Schirber (22 Aug 2013). "Synopsis: Spotlight on Photon-Photon Scattering". Physical Review Letters 111 (8): 080405. doi:10.1103/PhysRevLett.111.080405. PMID 24010419. Bibcode: 2013PhRvL.111h0405D. 
  7. ↑ "ATLAS observes light scattering off light". 2019-03-17. https://atlas.cern/updates/physics-briefing/atlas-observes-light-scattering-light. 
  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. doi:10.1093/mnras/stw2798. ISSN 0035-8711. 
  9. ↑ "Astronomers Report First Observational Evidence for Vacuum Birefringence | Astronomy | Sci-News.com" (in en-US). http://www.sci-news.com/astronomy/vacuum-birefringence-04410.html. 
  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. doi:10.1140/epjd/e2017-80290-7. ISSN 1434-6060. Bibcode: 2017EPJD...71..308F. 
  11. ↑ STAR Collaboration; Adam, J.; Adamczyk, L.; Adams, J. R.; Adkins, J. K.; Agakishiev, G.; Aggarwal, M. M.; Ahammed, Z. et al. (2021-07-27). "Measurement of e+e− Momentum and Angular Distributions from Linearly Polarized Photon Collisions". Physical Review Letters 127 (5): 052302. doi:10.1103/PhysRevLett.127.052302. PMID 34397228. Bibcode: 2021PhRvL.127e2302A. https://link.aps.org/doi/10.1103/PhysRevLett.127.052302. 
  12. ↑ "Collisions of Light Produce Matter/Antimatter from Pure Energy" (in en). https://www.bnl.gov/newsroom/news.php?a=119023. 
  13. ↑ "Colliding photons were spotted making matter. But are the photons 'real'?" (in en-US). 2021-08-09. https://www.sciencenews.org/article/colliding-photons-matter-particle-physics. 
  14. ↑ Taverna, Roberto; Turolla, Roberto; Muleri, Fabio; Heyl, Jeremy; Zane, Silvia; Baldini, Luca; Caniulef, Denis González; Bachetti, Matteo et al. (2022-05-18). "Polarized x-rays from a magnetar". Science 378 (6620): 646–650. doi:10.1126/science.add0080. PMID 36356124. Bibcode: 2022Sci...378..646T. 
  15. ↑ "X-ray polarisation probes extreme physics" (in en-GB). 2022-06-30. https://cerncourier.com/a/x-ray-polarisation-probes-extreme-physics/. 



Retrieved from "https://handwiki.org/wiki/index.php?title=Physics:Euler–Heisenberg_Lagrangian&oldid=3282296"