Nonlinear electrodynamics

{{Short description|Nonlinear generalizations of Maxwell electrodynamics}}

{{Technical|date=June 2025}}

In high-energy physics, nonlinear electrodynamics (NED or NLED) refers to a family of generalizations of Maxwell electrodynamics which describe electromagnetic fields that exhibit nonlinear dynamics. For a theory to describe the electromagnetic field (a U(1) gauge field), its action must be gauge invariant; in the case of $U(1)$, for the theory to not have Faddeev-Popov ghosts, this constraint dictates that the Lagrangian of a nonlinear electrodynamics must be a function of only $s\backslash equiv-\backslash frac14F\_\{\backslash alpha\; \backslash beta\}\; F^\{\backslash alpha\; \backslash beta\}$ (the Maxwell Lagrangian) and $p\backslash equiv-\backslash frac18\backslash epsilon^\{\backslash alpha\backslash beta\backslash gamma\backslash delta\}F\_\{\backslash alpha\; \backslash beta\}\; F\_\{\backslash gamma\backslash delta\}$ (where $\backslash epsilon$ is the Levi-Civita tensor).{{Cite journal |arxiv=2112.12118 |doi=10.1002/prop.202200092 |title=Introductory Notes on Non-linear Electrodynamics and its Applications |date=2022 |last1=Sorokin |first1=Dmitri P. |journal=Fortschritte der Physik |volume=70 |issue=7–8 }}{{Cite journal|doi=10.1515/zna-2024-0136 |title=Nonlinear electrodynamics and its possible connection to relativistic superconductivity: An example |date=2024 |last1=Bruce |first1=Stanley A. |journal=Zeitschrift für Naturforschung A |volume=79 |issue=11 |pages=1041–1046 |bibcode=2024ZNatA..79.1041B }} Notable NED models include the Born-Infeld model,{{Cite journal | doi=10.1098/rspa.1934.0059| title=Foundations of the New Field Theory| journal=Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences| volume=144| issue=852| pages=425–451| year=1934| last1=Born| first1=M.| last2=Infeld| first2=L.| bibcode=1934RSPSA.144..425B| doi-access=free}} the Euler-Heisenberg Lagrangian,{{cite journal | last1=Heisenberg | first1=W. | last2=Euler | first2=H. | title=Folgerungen aus der Diracschen Theorie des Positrons | journal=Zeitschrift für Physik | volume=98 | issue=11–12 | year=1936 | issn=1434-6001 | doi=10.1007/bf01343663 | pages=714–732 | language=de| bibcode=1936ZPhy...98..714H }} and the CP-violating $U(1)$ Chern-Simons theory $\backslash mathcal\{L\}=s+\backslash theta\; p$.{{Cite journal |arxiv=2101.00912 |doi=10.1007/JHEP06(2021)174 |title=Holographic DC conductivity for backreacted NLED in massive gravity |date=2021 |last1=Bi |first1=Shihao |last2=Tao |first2=Jun |journal=Journal of High Energy Physics |issue=6 |page=174 |bibcode=2021JHEP...06..174B }}{{Cite journal |arxiv=2101.08409 |doi=10.1103/PhysRevD.104.024033 |title=Weak deflection angle by electrically and magnetically charged black holes from nonlinear electrodynamics |date=2021 |last1=Fu |first1=Qi-Ming |last2=Zhao |first2=Li |last3=Liu |first3=Yu-Xiao |journal=Physical Review D |volume=104 |issue=2 |page=024033 |bibcode=2021PhRvD.104b4033F }}{{Cite arXiv |eprint=hep-th/0309108 |last1=Delphenich |first1=David |title=Nonlinear Electrodynamics and QED |date=2003 }}