非线性麦克斯韦理论概述
The Nonlinear Maxwell Theory---an Outline
摘要：
本文的目标是勾勒出一个更广泛的轮廓的数学结构中存在的非线性麦克斯韦理论在继续工作中提出的我以前的文章。特别是，我显示新类型的动态和静态的解决方案的非线性麦克斯韦方程组（NM）。我指出，由此产生的理论关系到相关电子的量子力学，因为它提供了一个介观的描述，如非电阻电荷传输，静态磁通量管，和电荷条纹的方式与现象学和微观原理相一致的现象。此外，我指出了一堆几何结构的内在理论。一方面，这些结构的存在表明，手头的方程可以被用作“探测工具”的纯几何探索低维流形。另一方面，在我看来，这些结构的全局方面是将相关电子系统的（量子）信息特征纳入非线性麦克斯韦理论框架的先决条件。
英文摘要：
The goal of this paper is to sketch a broader outline of the mathematical structures present in the Nonlinear Maxwell Theory in continuation of work presented in my previous articles. In particular, I display new types of both dynamic and static solutions of the Nonlinear Maxwell Equations (NM). I point out how the resulting theory ties to the Quantum Mechanics of Correlated Electrons inasmuch as it provides a mesoscopic description of phenomena like nonresistive charge transport, static magnetic flux tubes, and charge stripes in a way consistent with both the phenomenology and the microscopic principles. In addition, I point at a bunch of geometric structures intrinsic for the theory. On one hand, the presence of these structures indicates that the equations at hand can be used as `probing tools' for purely geometric exploration of low-dimensional manifolds. On the other hand, global aspects of these structures are in my view prerequisite to incorporating (quantum) informational features of Correlated Electron Systems within the framework of the Nonlinear Maxwell Theory.
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