Hey. When talking about invariance of a function f under some transformation T we mean that T(f)=f. But what is meant by invariance of an equation f=0? As far as I can see it makes sense to call an equation invariant when the transformed equation T(f)=T(0) is equivalent to the original equation f=0, or maybe just if T(f)=T(0) implies f=0.(adsbygoogle = window.adsbygoogle || []).push({});

To be specific, I am asking because the source free Yang-Mills equation D^{μ}F_{μν}=0 is said to be invariant under gauge transformations and i am wondering what exactly is meant by this. When preforming the gauge transformation U we obtain UD^{μ}F_{μν}U^{†}=0 which is equivalent to the original equation but not the same as the original equation.

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# I Invariance of an equation

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