Nonlinear electrodynamics

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. ^[1] For a theory to describe the electromagnetic field (a U(1) gauge field), its action must be gauge invariant; in the case of ${\displaystyle U(1)}$, 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 ${\displaystyle s\equiv -{\frac {1}{4}}F_{\alpha \beta }F^{\alpha \beta }}$ (the Maxwell Lagrangian) and ${\displaystyle p\equiv -{\frac {1}{8}}\epsilon ^{\alpha \beta \gamma \delta }F_{\alpha \beta }F_{\gamma \delta }}$ (where ${\displaystyle \epsilon }$ is the Levi-Civita tensor). ^{[1] [2] [3]} Notable NED models include the Born-Infeld model, ^[4] the Euler-Heisenberg Lagrangian, ^[5] and the CP-violating ${\displaystyle U(1)}$ Chern-Simons theory ${\displaystyle {\mathcal {L}}=s+\theta p}$. ^{[2] [6] [7]}

Some recent formulations also consider nonlocal extensions involving fractional U(1) holonomies on twistor space,^{[ citation needed ]} though these remain speculative.

References

1. Sorokin, Dmitri P. (2022). "Introductory Notes on Non-linear Electrodynamics and its Applications". Fortschritte der Physik. 70 (7–8). arXiv: 2112.12118 . doi:10.1002/prop.202200092.
2. Bi, Shihao; Tao, Jun (2021). "Holographic DC conductivity for backreacted NLED in massive gravity". Journal of High Energy Physics (6): 174. arXiv: 2101.00912 . Bibcode:2021JHEP...06..174B. doi:10.1007/JHEP06(2021)174.
3. Bruce, Stanley A. (2024). "Nonlinear electrodynamics and its possible connection to relativistic superconductivity: An example". Zeitschrift für Naturforschung A. 79 (11): 1041–1046. Bibcode:2024ZNatA..79.1041B. doi:10.1515/zna-2024-0136.
4. Born, M.; Infeld, L. (1934). "Foundations of the New Field Theory". Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences. 144 (852): 425–451. Bibcode:1934RSPSA.144..425B. doi: 10.1098/rspa.1934.0059 .
5. Heisenberg, W.; Euler, H. (1936). "Folgerungen aus der Diracschen Theorie des Positrons". Zeitschrift für Physik (in German). 98 (11–12): 714–732. Bibcode:1936ZPhy...98..714H. doi:10.1007/bf01343663. ISSN   1434-6001.
6. Fu, Qi-Ming; Zhao, Li; Liu, Yu-Xiao (2021). "Weak deflection angle by electrically and magnetically charged black holes from nonlinear electrodynamics". Physical Review D. 104 (2): 024033. arXiv: 2101.08409 . Bibcode:2021PhRvD.104b4033F. doi:10.1103/PhysRevD.104.024033.
7. Delphenich, David (2003). "Nonlinear Electrodynamics and QED". arXiv: hep-th/0309108 .