Again, I'm not sure whether this is the best place to post this question but its to do with gauge transformations, etc.(adsbygoogle = window.adsbygoogle || []).push({});

The question itself is rather stupid...

If we have a matrix U(g) (a Lie Group) and a vector φ inC(which is a scalar in spacetime) - does it make sense to use the chain rule thus:

[tex]{\partial}_\mu (U(g) \phi) = U(g){\partial}_\mu \phi + ({\partial}_\mu U(g)) \phi[/tex]

We are separately differentiating a matrix and vector - this seems very odd to me.

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# Differentiating a 'vector'

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