nLab
current

The term current in physics denotes either the gradient of the density of a field or of matter or the gradient of a wave function or of an order parameter. Most currents (though not all) in that sense satisfy some conservation laws, e.g. the current of electric charge, and so are known as conserved currents. This leads to the notion of conserved charge, see there.

In analysis, and specially in geometric measure theory, there is a different notion also called ‘current’. It is a generalized function (distribution in the sense of Schwartz and others) with values in differential forms. See at current (distribution theory) also integral current.

Regarding the material connotations it is not very surprising that the physics notion of current is related to distribution of stuff, and that analysis notion to distribution in Schwartz sense. Thus the two notions of distribution (and the third, distribution of hyperplanes or subspaces in tangent bundle on a manifold) and the two notions of current are related.

Last revised on July 26, 2016 at 06:54:03. See the history of this page for a list of all contributions to it.