कोवेरियंट इसके अंग्रेजी अर्थ का उदाहरण

Psycholinguistics The gauge covariant derivative is a variation of the covariant derivative used in general relativity.

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.

There are many ways to understand the gauge covariant derivative.

Another approach is to understand the gauge covariant derivative as a kind of connection, and more specifically, an affine connection.

For ordinary Lie algebras, the gauge covariant derivative on the space symmetries (those of the pseudo-Riemannian manifold and general relativity) cannot be intertwined with the internal gauge symmetries; that is, metric geometry and affine geometry are necessarily distinct mathematical subjects: this is the content of the Coleman–Mandula theorem.

In fluid dynamics, the gauge covariant derivative of a fluid may be defined as.

In gauge theory, which studies a particular class of fields which are of importance in quantum field theory, the minimally-coupled gauge covariant derivative is defined as.

Construction of the covariant derivative through gauge covariance requirement.

We can introduce the covariant derivative D_\mu in this context as a generalization of the partial derivative \partial_\mu which transforms covariantly under the Gauge transformation, i.

The requirement for D_\mu to transform covariantly is now translated in the condition.

and \bar \psi D_\mu \psi in the QED Lagrangian is therefore gauge invariant, and the gauge covariant derivative is thus named aptly.

On the other hand, the non-covariant derivative \partial_\mu would not preserve the Lagrangian's gauge symmetry, since.