Noether's theorem: Difference between revisions

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Revision as of 01:18, 30 July 2004

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which is called the '''Noether current''' associated with the [[symmetry]]. The continuity equation tells us if we [[integrate]] this current over a [[space-like]] slice, we get a [[conservation law|conserved]] quantity called the [[Noether charge]] (provided, of course, if M is [[compact|noncompact]], the currents fall off sufficiently fast at infinity).

This is not generally well-known, but Noether's theorem is really a reflection of the relation between the boundary conditions and the variational principle. Assuming no boundary terms in the action, Noether's theorem implies that

<math>\int_{\partial N}ds_\mu J^\mu=0</math>

Noether's theorem is an [[on shell]] theorem.

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