Conserved current

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

where ${\displaystyle Q=\int _{V}j^{0}dV}$ is the conserved quantity.

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