标题： 自对偶非线性电动力学的对偶性 显示英文标题

标题： Dualities of Self-Dual Nonlinear Electrodynamics

摘要： 对于任何具有“自对偶”性质（电磁$U(1)$-对偶不变）的因果非线性电动力学理论，由与粒子力学拉格朗日和哈密顿相关的${\bf R}^+$上的函数$\{\ell,h\}$构造出拉格朗日密度和哈密顿密度的勒让德对偶对$\{\mathcal{L},\mathcal{H}\}$。 我们展示了将 `对偶性` 关系应用于$\ell$和$h$时，如何意味着$\mathcal{L}$和$\mathcal{H}$通过适当变量对之间的简单映射相关联。我们还讨论了Born的“勒让德自对偶性”以及一种新的“$\Phi$-宇称”对偶性的含义。我们的结果通过许多例子进行了说明。 显示英文摘要

摘要： For any causal nonlinear electrodynamics theory that is "self-dual" (electromagnetic $U(1)$-duality invariant), the Legendre-dual pair of Lagrangian and Hamiltonian densities $\{\mathcal{L},\mathcal{H}\}$ are constructed from functions $\{\ell,h\}$ on ${\bf R}^+$ related to a particle-mechanics Lagrangian and Hamiltonian. We show how a `duality' relating $\ell$ to $h$ implies that $\mathcal{L}$ and $\mathcal{H}$ are related by a simple map between appropriate pairs of variables. We also discuss Born's "Legendre self-duality" and implications of a new "$\Phi$-parity" duality. Our results are illustrated with many examples.