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This is an interesting question that popped through my mind. Some of us should know what is meant by „gauge transformations”, „gauge invariance/symmetry” and are used to seeing these terms whenever lectures on quantum field theory are read. But the electromagnetic field in vacuum (described in a specially relativistic fashion by the tensor ##F_{\mu\nu}##) is a classical one (i.e. it exists also in a non quantum setting), so one has the right to ask. Given E,B or ##F##, what does it mean to say about the "classical electromagnetism" to be U(1) invariant?