非线性电磁理论的本构关系和薛定谔公式
Constitutive relations and Schroedinger's formulation of nonlinear electromagnetic theories
摘要：
我们提出了一个系统的研究电磁非线性和高阶导数扩展。我们澄清时，作用泛函S[F]可以明确地从任意（不一定是自对偶）的非线性运动方程。我们表明，“变形扭曲的自对偶条件”的建议起源于超引力反项的背景下，实际上是讨论自对偶理论从变分原理开始所需的一般框架。本文将Born-Infeld理论的Schroedinger公式推广到非线性和高阶导数理论，对于后者，以及更一般的非线性理论，我们导出了相应的变形扭曲自对偶条件的封闭形式表达式。这意味着进入这些对偶条件并导致玻恩-因菲尔德理论的超几何表达式满足一个隐藏的四次方程。
英文摘要：
We present a systematic study of nonlinear and higher derivatives extensions of electromagnetism. We clarify when action functionals S[F] can be explicitly obtained from arbitrary (not necessarily self-dual) nonlinear equations of motion. We show that the "Deformed twisted self-duality condition" proposal originated in the context of supergravity counterterms is actually the general framework needed to discuss self-dual theories starting from a variational principle. We generalize to nonlinear and higher derivatives theories Schroedinger formulation of Born-Infeld theory, and for the latter, and more in general for nonlinear theories, we derive a closed form expression of the corresponding deformed twisted self-duality conditions. This implies that the hypergeometric expression entering these duality conditions and leading to Born-Infeld theory satisfies a hidden quartic equation.
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