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In order to be clear, I will write down every component explicitly. Also, I assume Euclidean metric in this post, so that spacetime indices are written as $i,j$ rather than $\mu, \nu$. Following Wiki, ...

If we consider the usual formal construction of a path integral over fields with gauge symmetries e.g as in Weinbergs "The Quantum Theory of Fields - Volume 2" the notion of gauge invariance ...