Gauge Potential Transformations

michael879

Can someone please show me what transformation the lagrangian is invariant under in a theory with just an SU(N) gauge field (with or w/o a source term I don't think it matters). I tried to find this on my own and I got some confusing answers.

Except for U(1), every source I found said that the transformation is of the form $A_\mu \rightarrow UA_\mu U^\dagger - iU\partial_\mu U^\dagger$. However, this clearly doesn't apply to a U(1) gauge field where the transformation is $A_\mu \rightarrow A + \partial_\mu f$

*edit* I just realized that they are actually the same, but I can't figure how to delete this thread.

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