When a classical field is varied so that ##\phi ^{'}=\phi +\delta \phi## the spatial partial derivatives of the field is often written $$\partial _{\mu }\phi ^{'}=\partial _{\mu }(\phi +\delta \phi )=\partial _{\mu }\phi +\partial _{\mu }\delta \phi $$. Often times the next step is to switch the order of the variation and the partial derivative to get ##\partial _{\mu }\phi ^{'}=\partial _{\mu }\phi +\delta (\partial _{\mu }\phi )##. What justifies the replacement of ##\partial_{\mu }(\delta\phi )## by ##\delta (\partial _{\mu }\phi )##?(adsbygoogle = window.adsbygoogle || []).push({});

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# I Derivative of a Variation vs Variation of a Derivative

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