This question is from K. Huang, Quantum Field Theory: from operators to path integrals.(adsbygoogle = window.adsbygoogle || []).push({});

He says that, under a continuous infinitesimal transformation,

[itex]\phi[/itex](x)->[itex]\phi[/itex](x)+[itex]\delta\phi[/itex]

the change of the Lagrangian density must be in the from

[itex]\delta[/itex]L=[itex]∂^{\mu}[/itex][itex]W_{\mu}[/itex](x)

It is easily understood that this quantity must be Lorentz-invariant, but why should only be this form, not others (e.g. without derivatives).

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# About Noether's theorem

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