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charge of a conserved current

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Context

Variational calculus

Physics

physics, mathematical physics, philosophy of physics

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theory (physics), model (physics)

experiment, measurement, computable physics

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Definition

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

For jΩ n1,pj \in \Omega^{n-1,p} a conserved current and ΣX\Sigma \subset X a submanifold of dimension n1n-1, the charge of jj relative to Σ\Sigma is the integral

Q Σ= Σj. Q_\Sigma = \int_\Sigma j \,.

Examples

gauge field: models and components

physicsdifferential geometrydifferential cohomology
gauge fieldconnection on a bundlecocycle in differential cohomology
instanton/charge sectorprincipal bundlecocycle in underlying cohomology
gauge potentiallocal connection differential formlocal connection differential form
field strengthcurvatureunderlying cocycle in de Rham cohomology
gauge transformationequivalencecoboundary
minimal couplingcovariant derivativetwisted cohomology
BRST complexLie algebroid of moduli stackLie algebroid of moduli stack
extended Lagrangianuniversal Chern-Simons n-bundleuniversal characteristic map

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