论文标题
从折磨纸的弹性理论降低了kaluza-klein尺寸
Kaluza-Klein Dimensional Reduction From Elasticity Theory of Crumpled Paper
论文作者
论文摘要
在上个世纪，使用降低维度概念的两种独立理论已经独立发展。第一种被称为föppl-vonKàrmàn理论，使用riemannian几何形状和连续力学来研究薄弹性结构的形状，这些结构可能变得像皱纹纸一样复杂。第二种，称为Kaluza-Klein理论，使用Minkowskian几何形状和一般相对论来统一相同形式的基本相互作用和重力。在这里，我们在这两种理论之间绘制了一个相似之处，以尝试使用板块弹性理论的概念来恢复爱因斯坦 - 马克斯韦尔方程。我们认为，Kaluza-Klein理论属于与三维弹性相同的概念群体群体，而这会导致二维弹性板的Föppl-VonKàrmàn理论。我们利用这种类比来在弹性理论框架中开发替代性的kaluza-klein形式主义，其中引力和电磁场分别与拉伸样和弯曲样变形有关。我们表明，我们的尺寸还原方法使我们能够检索引力，电磁和狄拉克纺纱田的拉格朗日密度以及质量和电荷来源的拉格朗日密度。
During the last century, two independent theories using the concept of dimensional reduction have been developed independently. The first, known as Föppl-von Kàrmàn theory, uses Riemannian geometry and continuum mechanics to study the shaping of thin elastic structures which could become as complex as crumpled paper. The second one, known as Kaluza-Klein theory, uses Minkowskian geometry and general relativity to unify fundamental interactions and gravity under the same formalism. Here we draw a parallel between these two theories in an attempt to use concepts from elasticity theory of plates to recover the Einstein-Maxwell equations. We argue that Kaluza-Klein theory belongs to the same conceptual group of theories as three-dimensional elasticity, which upon dimensional reduction leads to the Föppl-von Kàrmàn theory of two-dimensional elastic plates. We exploit this analogy to develop an alternative Kaluza-Klein formalism in the framework of elasticity theory in which the gravitational and electromagnetic fields are respectively associated with stretching-like and bending-like deformations. We show that our approach of dimensional reduction allows us to retrieve the Lagrangian densities of both gravitational, electromagnetic and Dirac spinors fields as well as the Lagrangian densities of mass and charge sources.
