费米-伯恩-因费尔德电动力学：一种具有物理规范的非线性理论
Fermi--Born--Infeld electrodynamics: a nonlinear theory with physical gauge
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中文总结 AI 辅助
该研究构建费米-伯恩-因费尔德电动力学，通过特定结构消除规范冗余，推导出场方程，利用非线性稳定纵向模式，计算自旋密度，保留费米原始物理规范并纳入正则化特征，为强场电磁现象描述提供候选理论。
中文摘要 AI 辅助
我们通过纳入直接依赖于四势\(A_\mu\)而非场强\(F_{\mu\nu}\)的伯恩-因费尔德结构，构建了费米电动力学的非线性扩展。所得理论即费米-伯恩-因费尔德（FBI）电动力学，通过将洛伦兹规范提升为动力学条件消除了\(U(1)\)规范冗余。拉格朗日量由类度规张量\(g_{\mu\nu}=\eta_{\mu\nu}+2\kappa\,\partial_{(\mu}A_{\nu)}\)的行列式构建。推导出场方程并表明洛伦兹条件从延迟边界条件和正能量谱要求动态出现。非线性改变纵向模式传播，通过类似瓦因施泰因机制，非线性自相互作用可能稳定纵向模式。还计算了诺特定流的自旋密度并讨论其性质。FBI理论保留了费米原始表述的物理规范并纳入伯恩-因费尔德电动力学的正则化特征，有望描述强场区域电磁现象。
英文摘要
We construct a nonlinear extension of Fermi's electrodynamics by incorporating a Born--Infeld structure that depends directly on the four-potential $A_μ$ rather than on the field strength $F_{μν}$. The resulting theory, which we call Fermi--Born--Infeld (FBI) electrodynamics, eliminates the $U(1)$ gauge redundancy by elevating the Lorenz gauge to a dynamical condition. The Lagrangian is built from the determinant of a metric-like tensor $g_{μν} = η_{μν} + 2κ\, \partial_{(μ} A_{ν)}$, ensuring that the canonical energy--momentum tensor and the spin density remain unique and free of gauge ambiguities. We derive the field equations, which reduce to $\partial_ν(\sqrt{-g}\, g^{μν}) = 0$, and show that the Lorenz condition $\partial_μA^μ= 0$ emerges dynamically from retarded boundary conditions and the requirement of a positive-energy spectrum. The nonlinearities modify the propagation of longitudinal modes; we argue, via a Vainshtein-like mechanism, that the nonlinear self-interactions may stabilize the longitudinal mode, opening the possibility of a stable massive scalar photon under extreme field conditions. We also compute the spin density from the Noether current and discuss its properties. The FBI theory preserves the physical gauge of Fermi's original formulation while incorporating the regularization features of Born--Infeld electrodynamics, making it a candidate for describing electromagnetic phenomena in strong-field regimes.
