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gauge covariant derivative : ウィキペディア英語版
gauge covariant derivative
The gauge covariant derivative is a generalization of the covariant derivative used in general relativity. If a theory has gauge transformations, it means that some physical properties of certain equations are preserved under those transformations. Likewise, the gauge covariant derivative is the ordinary derivative modified in such a way as to make it behave like a true vector operator, so that equations written using the covariant derivative preserve their physical properties under gauge transformations.
==Fluid dynamics==
In fluid dynamics, the gauge covariant derivative of a fluid may be defined as
: \nabla_t \mathbf:= \partial_t \mathbf + (\mathbf \cdot \nabla) \mathbf
where \mathbf is a velocity vector field of a fluid.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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