Irrotational

As irrotational or conservative vector field is called in physics and potential theory, in which the line integral

For any self-contained boundary curves S always returns the value zero.

Vertebrae are free, for example, the stationary electric field and the gravitational field, but also fields such as the velocity field of a potential flow.

We interpret as a force field, so the above integral is the entire ring along the boundary curve of S against the force of work done, then - and only then - will be equal to zero and thus independent of the path if:

Vortex -free vector fields can always be formulated as a gradient of a scalar field underlying:

So that also applies: