Euler–Heisenberg Lagrangian
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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 ...
of
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 classical c ...
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 dis ...
. 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 Theorie' ...
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 tera ...
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, :\mathcal =-\mathcal -\frac\int_^\exp\left(-m^s\right)\left es)^\frac\mathcal-\frac(es)^\mathcal - 1\rightfrac. 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 Particle physics or high energy physics is the study of fundamental particles and forces that constitute matter and radiation. The fundamental particles ...
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 polariz ...
of
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 nuclei. It consists of the shortest wavelength electromagnetic waves, typically ...
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, so they always ...
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 to ...
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 Ferra ...
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 fir ...
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 interes ...
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 The European Organization for Nuclear Research, known as CERN (; ; ), is an intergovernmental organization that operates the largest particle physics laboratory in the world. Established in 1954, it is based in a northwestern suburb of Gene ...
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 birefring ...
. 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 Ea ...
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 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 ...
. 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 an ...
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 an ...
, the Breit–Wheeler process 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


See also

*
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 birefring ...
* Circular dichroism *
Chiral magnetic effect Chiral magnetic effect (CME) is the generation of electric current along an external magnetic field induced by chirality imbalance. Fermions are said to be chiral if they keep a definite projection of spin quantum number on momentum. The CME is a ...
*
Schwinger limit In quantum electrodynamics (QED), the Schwinger limit is a scale above which the electromagnetic field is expected to become nonlinear. The limit was first derived in one of QED's earliest theoretical successes by Fritz Sauter in 1931 and discu ...
*
Schwinger effect The Schwinger effect is a predicted physical phenomenon whereby matter is created by a strong electric field. It is also referred to as the Sauter–Schwinger effect, Schwinger mechanism, or Schwinger pair production. It is a prediction of quantu ...
* Uehling potential *
Electric polarization In classical electromagnetism, polarization density (or electric polarization, or simply polarization) is the vector field that expresses the density of permanent or induced electric dipole moments in a dielectric material. When a dielectric is ...
*
Kerr effect The Kerr effect, also called the quadratic electro-optic (QEO) effect, is a change in the refractive index of a material in response to an applied electric field. The Kerr effect is distinct from the Pockels effect in that the induced index chang ...


References

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