The **gauge covariant derivative** is like 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.

Read more about Gauge Covariant Derivative: Fluid Dynamics, Gauge Theory, General Relativity

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**Gauge Covariant Derivative**- General Relativity

... In general relativity, the

**gauge covariant derivative**is defined as where is the Christoffel symbol ...

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