In physics, the Euler–Heisenberg Lagrangian describes the

non-linear dynamics In mathematics, a dynamical system is a system in which a function describes the time dependence of a point in an ambient space. Examples include the mathematical models that describe the swinging of a clock pendulum, the flow of water in a ...

electromagnetic field An electromagnetic field (also EM field or EMF) is a classical (i.e. non-quantum) field produced by (stationary or moving) electric charges. It is the field described by classical electrodynamics (a classical field theory) and is the classica ...

s in

vacuum A vacuum is a space devoid of matter. The word is derived from the Latin adjective ''vacuus'' for "vacant" or " void". An approximation to such vacuum is a region with a gaseous pressure much less than atmospheric pressure. Physicists often di ...

. It was first obtained by

Werner Heisenberg Werner Karl Heisenberg () (5 December 1901 – 1 February 1976) was a German theoretical physicist and one of the main pioneers of the theory of quantum mechanics. He published his work in 1925 in a breakthrough paper. In the subsequent series ...

and

Hans Heinrich Euler Hans Heinrich Euler (b. 6 October 1909 in Merano, d. 1941) was a German physicist. He received his PhD in 1935 at the University of Leipzig under Werner Heisenberg with a thesis ''Über die Streuung von Licht an Licht nach der Diracschen Theor ...

in 1936. By treating the vacuum as a medium, it predicts rates of

quantum electrodynamics In particle physics, quantum electrodynamics (QED) is the relativistic quantum field theory of electrodynamics. In essence, it describes how light and matter interact and is the first theory where full agreement between quantum mechanics and spec ...

(QED)

light Light or visible light is electromagnetic radiation that can be perceived by the human eye. Visible light is usually defined as having wavelengths in the range of 400–700 nanometres (nm), corresponding to frequencies of 750–420 te ...

interaction processes.

Physics

It takes into account

vacuum polarization In quantum field theory, and specifically quantum electrodynamics, vacuum polarization describes a process in which a background electromagnetic field produces virtual electron–positron pairs that change the distribution of charges and curr ...

to one loop, and is valid for electromagnetic fields that change slowly compared to the inverse electron mass, :

frac.

Here is the electron mass, the electron charge,

\mathcal=\frac\left(\mathbf^2 - \mathbf^2\right)

, and

\mathcal=\mathbf\cdot\mathbf

. In the weak field limit, this becomes :

\mathcal = \frac\left(\mathbf^-\mathbf^\right)+\frac\left left(\mathbf^2 - \mathbf^2\right)^ + 7 \left(\mathbf\cdot\mathbf\right)^\right

It describes

photon–photon scattering Two-photon physics, also called gamma–gamma physics, is a branch of particle physics that describes the interactions between two photons. Normally, beams of light pass through each other unperturbed. Inside an optical material, and if the inten ...

in QED;

Robert Karplus Robert Karplus (February 23, 1927 – March 20, 1990) was a theoretical physicist and leader in the field of science education. Early life Robert Karplus was born in Vienna, where he lived until the German occupation of Austria in 1938. He emigrate ...

and Maurice Neuman calculated the full amplitude, which is very small.

Experiments

Delbrück scattering Delbrück scattering, the deflection of high-energy photons in the Coulomb field of nuclei as a consequence of vacuum polarization, was observed in 1975. The related process of the scattering of light by light, also a consequence of vacuum polari ...

gamma ray A gamma ray, also known as gamma radiation (symbol γ or \gamma), is a penetrating form of electromagnetic radiation arising from the radioactive decay of atomic nucleus, atomic nuclei. It consists of the shortest wavelength electromagnetic wav ...

s was observed in 1953 by Robert Wilson.

Photon A photon () is an elementary particle that is a quantum of the electromagnetic field, including electromagnetic radiation such as light and radio waves, and the force carrier for the electromagnetic force. Photons are Massless particle, massless ...

splitting in strong

magnetic field A magnetic field is a vector field that describes the magnetic influence on moving electric charges, electric currents, and magnetic materials. A moving charge in a magnetic field experiences a force perpendicular to its own velocity and t ...

s was measured in 2002.

PVLAS PVLAS (Polarizzazione del Vuoto con LASer, "polarization of the vacuum with laser") aims to carry out a test of quantum electrodynamics and possibly detect dark matter at the Department of Physics and National Institute of Nuclear Physics in Ferrar ...

is searching for vacuum polarization of

laser A laser is a device that emits light through a process of optical amplification based on the stimulated emission of electromagnetic radiation. The word "laser" is an acronym for "light amplification by stimulated emission of radiation". The firs ...

beams crossing magnetic fields to detect effects from

axion An axion () is a hypothetical elementary particle postulated by the Peccei–Quinn theory in 1977 to resolve the strong CP problem in quantum chromodynamics (QCD). If axions exist and have low mass within a specific range, they are of interest ...

dark matter Dark matter is a hypothetical form of matter thought to account for approximately 85% of the matter in the universe. Dark matter is called "dark" because it does not appear to interact with the electromagnetic field, which means it does not ab ...

. No signal has been found and searches continue. OSQAR at CERN is also studying vacuum

birefringence Birefringence is the optical property of a material having a refractive index that depends on the polarization and propagation direction of light. These optically anisotropic materials are said to be birefringent (or birefractive). The birefrin ...

. In 2016 a team of astronomers from Italy, Poland, and the U.K. reported observations of the light emitted by a neutron star (

pulsar A pulsar (from ''pulsating radio source'') is a highly magnetized rotating neutron star that emits beams of electromagnetic radiation out of its magnetic poles. This radiation can be observed only when a beam of emission is pointing toward E ...

RX J1856.5−3754 RX J1856.5−3754 (also called RX J185635−3754, RX J185635−375, and various other designations) is a neutron star in the constellation Corona Australis. At approximately 400 light-years from Earth, it is the closest neutron star disco ...

). 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 Degree of polarization (DOP) is a quantity used to describe the portion of an electromagnetic wave which is polarized. A perfectly polarized wave has a DOP of 100%, whereas an unpolarized wave has a DOP of 0%. A wave which is partially polarize ...

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. In 2019 the observation of photon–photon scattering was reported by the

ATLAS Collaboration ATLAS is the largest general-purpose particle detector experiment at the Large Hadron Collider (LHC), a particle accelerator at CERN (the European Organization for Nuclear Research) in Switzerland. The experiment is designed to take advantage o ...

. In July 2021 the first known observation of vacuum birefringence was reported by the

STAR experiment The STAR detector (for Solenoidal Tracker at RHIC) is one of the four experiments at the Relativistic Heavy Ion Collider (RHIC) in Brookhaven National Laboratory, United States. The primary scientific objective of STAR is to study the formation a ...

at the

Relativistic Heavy Ion Collider The Relativistic Heavy Ion Collider (RHIC ) is the first and one of only two operating heavy- ion colliders, and the only spin-polarized proton collider ever built. Located at Brookhaven National Laboratory (BNL) in Upton, New York, and used by ...

, the

Breit–Wheeler process The Breit–Wheeler process or Breit–Wheeler pair production is a physical process in which a positron–electron pair is created from the collision of two photons. It is the simplest mechanism by which pure light can be potentially transformed ...

was also studied although only evidence was reported In May 2022 the first study of

IXPE Imaging X-ray Polarimetry Explorer, commonly known as IXPE or SMEX-14, is a space observatory with three identical telescopes designed to measure the polarization of cosmic X-rays of black holes, neutron stars, and pulsars. The observatory ...

has hinted the possibility of vacuum birefringence on

4U 0142+61 4U 0142+61 is a magnetar at an approximate distance of from Earth, located in the constellation Cassiopeia. In an article published in ''Nature'' on April 6, 2006, Deepto Chakrabarty ''et al.'' of MIT revealed that a circumstellar disk ...

References

{{DEFAULTSORT:Euler-Heisenberg Lagrangian Quantum electrodynamics Electromagnetic radiation Werner Heisenberg

Physics

Experiments

See also

References