# nLab charge of a conserved current

Contents

### Context

#### Variational calculus

variational calculus

# Contents

## 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

gauge field: models and components

Last revised on March 26, 2014 at 09:05:52. See the history of this page for a list of all contributions to it.