Noether's theorem: Difference between revisions

Revision as of 16:35, 14 May 2004

Revision as of 07:23, 16 May 2004

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Suppose given [[boundary condition]]s, which are basically a specification of the value of &phi; at the [[boundary]] of M is [[compact]], or some limit on &phi; as x approaches <math>\infty</math>; this will help in doing [[integration by parts]]). We can denote by N the [[subset]] of <math>\mathcal{C}</math> consisting of functions, &phi; such that all [[functional derivative]]s of S at &phi; are zero and &phi; satisfies the given boundary conditions.

Now, suppose we have an [[infinitesimal]] [[Transformation (mathematics)|transformation]] on <math>\mathcal{C}</math>, given by a [[functional derivative]], &delta; such that

:<math>\delta\int_N d^nx\mathcal{L}=\int_{\partial N}ds_\mu f^\mu(\phi(x),\partial\phi,\partial\partial\phi,...)</math>