外反对称微分形式和演化反对称微分形式在数学物理中的作用
Role of exterior and evolutionary skew-symmetric differential forms in mathematical physics
摘要：
反对称微分形式在数学物理中的一个作用与它们反映守恒定律的性质有关。封闭的外部形式对应于物理场的守恒定律，而演化形式对应于物质介质的守恒定律。反对称微分形式可以描述任何对象的共轭性（对应于守恒律）。封闭的外部形式描述共轭的对象。而演化形式则描述了对象的共轭化和得到共轭对象的过程，其基础是变形流形。从演化形式中得到封闭的外部形式。这表明物质媒介产生物理场。演化外形式与封闭外形式的关系揭示了数学物理方程与场论方程的关系。这就解释了场论的假设。如果存在对称性，共轭是可能的。封闭外形式的对称性是物理场守恒定律成立的条件，也是场论的内对称性。而对偶形式的对称性（由于物质介质的自由度）是场论方程的外部对称性。这表明了场论的内部对称性和外部对称性之间的联系。
英文摘要：
A role of skew-symmetric differential forms in mathematical physics relates to the fact that they reflect the properties of conservation laws. The closed exterior forms correspond to the conservation laws for physical fields, whereas the evolutionary forms correspond to the conservation laws for material media. Skew-symmetric differential forms can describe a conjugacy of any objects (that correspond to the conservation laws). The closed exterior forms describe conjugated objects. And the evolutionary forms, whose basis are deforming manifolds, describe the process of conjugating objects and obtaining conjugated objects. From the evolutionary forms the closed exterior forms are obtained. This shows that material media generate physical fields. The relation between evolutionary and closed exterior forms discloses the relation between the equations of mathematical physics and field theories. This explains the field theory postulates. Conjugacy is possible if there is symmetry. Symmetries of closed exterior forms, which are conditions of fulfilment of the conservation laws for physical fields, are interior symmetries of field theories. And symmetries of dual forms (due to the degrees of freedom of material media) are external symmetries of the equations of field theories. This shows connection between internal and external symmetries of field theories.
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