Nonlinear electrodynamics
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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.cite-ref-introductory-notes-1-0[1] 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 ) {\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 s ≡ ≡ − − 1 4 F α α β β F α α β β {\displaystyle s\equiv -{\frac {1}{4}}F_{\alpha \beta }F^{\alpha \beta }} (the Maxwell Lagrangian) and p ≡ ≡ − − 1 8 ϵ ϵ α α β β γ γ δ δ F α α β β F γ γ δ δ {\displaystyle p\equiv -{\frac {1}{8}}\epsilon ^{\alpha \beta \gamma \delta }F_{\alpha \beta }F_{\gamma \delta }} (where ϵ ϵ {\displaystyle \epsilon } is the Levi-Civita tensor).cite-ref-introductory-notes-1-1[1]cite-ref-holographic-dc-2-0[2]cite-ref-3[3] Notable NED models include the Born-Infeld model,cite-ref-m-born-l-infeld-4-0[4] the Euler-Heisenberg Lagrangian,cite-ref-5[5] and the CP-violating U ( 1 ) {\displaystyle U(1)} Chern-Simons theory L = s + θ θ p {\displaystyle {\mathcal {L}}=s+\theta p} .cite-ref-holographic-dc-2-1[2]cite-ref-6[6]cite-ref-7[7]
Some recent formulations also consider nonlocal extensions involving fractional U(1) holonomies on twistor space, though these remain speculative.
References
cite-note-66. ↑ citereffuzhaoliu2021Fu, 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.