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 in 1936. By treating the vacuum as a medium, it predicts rates of quantum electrodynamics (QED) light interaction processes.[clarification needed]
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:
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.
A team of astronomers from Italy, Poland, and the U.K. has reported in 2016 observations of the light emitted by a neutron star (pulsar RX J1856.5−3754). The star is surrounded by a very strong magnetic field (1013G), and one expects birefringence 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.
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- R. P. Mignani, V. Testa, D. González Caniulef, R. Taverna, R. Turolla, S. Zane, and K. Wu, "Evidence for vacuum birefringence from the first optical-polarimetry measurement of the isolated neutron star RX J1856.5−3754", Month. Not. Roy. Astron. Soc. 465 (2017) 492, published online 02 Nov 2016.
- Fan, X., Kamioka, S., Inada, T., Yamazaki, T., Namba, T., Asai, S., ... & Kawaguchi, K. (2017). The OVAL experiment: A new experiment to measure vacuum magnetic birefringence using high repetition pulsed magnets. arXiv preprint arXiv:1705.00495.