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How do we know the generator of U(1) symmetry is the operator of electric charge.Is this observation(the value defined by the operator) being the reserved observation deducing from Noether theorem(considering U(1) symmetry).And also how we know this Noether reserved observation were electric charge?

(I have known that from U(1) symmetry we can deduce the Dirac-Maxwell Lagrangian,but I do not understand the relation between the generator and ''physical'' electric charge)

Thank you very much for your kind helping.

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# How do we know generator of U(1) is operator of electric charge?

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