nLab
charge

Definition

Let $X$ be a (spacetime) smooth manifold of dimension $n$ , $E\to X$ a field bundle and $L\in {\Omega }^{n,0}(j_{\mathrm{\infty }}E)$ a Lagrangian.

For $j\in {\Omega }^{n-1,p}$ a conserved current and $\Sigma \subset X$ a submanifold of dimension $n-1$, the charge of $j$ relative to $\Sigma$ is the integral

$$Q_{\Sigma }={\int }_{\Sigma }j.$$Q_\Sigma = \int_\Sigma j \,.

Examples

• electric charge, magnetic charge