nLab charge of a conserved current

Definition

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

$$Q_\Sigma = \int_\Sigma j \,.$$

Examples

• electric charge, magnetic charge

• mass, spin

• D-term

• supercharge

Related concepts

• Noether's theorem

• central charge

gauge field: models and components

physics	differential geometry	differential cohomology
gauge field	connection on a bundle	cocycle in differential cohomology
instanton/charge sector	principal bundle	cocycle in underlying cohomology
gauge potential	local connection differential form	local connection differential form
field strength	curvature	underlying cocycle in de Rham cohomology
gauge transformation	equivalence	coboundary
minimal coupling	covariant derivative	twisted cohomology
BRST complex	Lie algebroid of moduli stack	Lie algebroid of moduli stack
extended Lagrangian	universal Chern-Simons n-bundle	universal characteristic map