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- Thread starter quickAndLucky
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haushofer

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I guess my question is "why do variations and derivatives commute?"

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samalkhaiat

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haushofer answered your question correctly. The variation [itex]\delta[/itex] measures the change in the functional form of a field at a fixed coordinate value. So, if you define the field [itex]\psi_{\mu}(x) = \partial_{\mu}\phi (x)[/itex], then it follows from the definition of [itex]\delta[/itex] that [tex]\delta \psi_{\mu}(x) = \psi_{\mu}^{'}(x) - \psi_{\mu}(x),[/tex] orI guess my question is "why do variations and derivatives commute?"

[tex]\delta (\partial_{\mu}\phi )(x) = \partial_{\mu}\phi^{'}(x) - \partial_{\mu}\phi(x) = \partial_{\mu}\left(\phi^{'} - \phi \right) (x) = \partial_{\mu}( \delta \phi )(x) .[/tex]

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