Conserved current

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In physics a conserved current is a current, ${\displaystyle j^{\mu }}$, that satisfies the continuity equation ${\displaystyle \partial _{\mu }j^{\mu }=0}$. The continuity equation represents a conservation law, hence the name.

Indeed, integrating the continuity equation over a volume ${\displaystyle V}$, large enough to have no net currents through its surface, leads to the conservation law$${\displaystyle {\frac {\partial }{\partial t}}Q=0\;,}$$where ${\textstyle Q=\int _{V}j^{0}dV}$ is the conserved quantity.

In gauge theories the gauge fields couple to conserved currents. For example, the electromagnetic field couples to the conserved electric current.