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广义协变性

理论物理学中,广义协变性(又称为微分同胚协变性广义不变性)为物理定律的形式在任意微分坐标变换下保持不变。其精神在于坐标并非先验地存在于自然中,而是人们欲描述自然所伴随的人工产物;也因此不应在基本物理定律中具有实质物理意义。

以广义协变性表示的物理定律,在所有坐标系中皆应保持相同的数学形式。欲达成此目标,通常会以张量场来描述物理量。经典电磁学(非量子的)为其中一项例子。阿尔伯特·爱因斯坦在1905年提出的狭义相对论以及1915年提出的广义相对论皆采用广义协变性原则[1];然而前者的例子局限在平直时空惯性参考系,为全域的洛伦兹协变性。后者则推广为局域的洛伦兹协变性,以适用所有参考系,并能解释加速运动重力现象。

经典统一场论的大部分工作着墨于将广义相对论推广至涵盖电磁学等物理现象,其推论基础亦即广义协变性。

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广义协变性
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