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Evolutionary forms: The generation of differential-geometrical structures. (Symmetries and Conservation laws.)

机译:进化形式:差异几何的产生   结构。 (对称性和保护法。)

摘要

Evolutionary forms, as well as exterior forms, are skew-symmetricdifferential forms. But in contrast to the exterior forms, the basis ofevolutionary forms is deforming manifolds (with unclosed metric forms). Suchforms possess a peculiarity, namely, the closed inexact exterior forms areobtained from that. The closure conditions of inexact exterior form (vanishing the differentialsof exterior and dual forms) point out to the fact that the closed inexactexterior form is a quantity conserved on pseudostructure having the dual formas the metric form. We obtain that the closed inexact exterior form andcorresponding dual form made up a conservative object, i.e. a quantityconserved on pseudostructure. Such conservative object corresponds to theconservation law and is a differential-geometrical structure. Transition from the evolutionary form to the closed inexact exterior formdescribes the process of generating the differential-geometrical structures.This transition is possible only as a degenerate transformation, the conditionof which is a realization of a certain symmetry. Physical structures that made up physical fields are suchdifferential-geometrical structures. And they are generated by material systems(medias). Relevant symmetries are caused by the degrees of freedom of materialsystem.
机译:演化形式以及外部形式都是倾斜对称的差分形式。但是与外部形式相反,进化形式的基础是变形流形(具有未封闭的公制形式)。这种形式具有特殊性,即从中获得封闭的不精确的外部形式。不精确的外部形式的封闭条件(消除了外部形式和对偶形式的差异)指出了这样一个事实,即不精确的外部形式的封闭性是具有双重形式公制形式的伪结构上守恒的数量。我们获得了封闭的不精确的外部形式和相应的对偶形式组成了一个保守的对象,即在伪结构上守恒的一个量。这种保守的对象符合守恒定律,并且是微分几何结构。从演化形式到封闭的不精确外部形式的过渡描述了生成微分几何结构的过程。这种过渡仅可能是简并变换,其条件是一定对称性的实现。构成物理场的物理结构就是这种微分几何结构。它们是由物质系统(媒体)生成的。相关的对称性是由材料系统的自由度引起的。

著录项

  • 作者

    Petrova, L. I.;

  • 作者单位
  • 年度 2005
  • 总页数
  • 原文格式 PDF
  • 正文语种 {"code":"en","name":"English","id":9}
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