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1$\begingroup$ Ok, so I can consider it just a mere mathematical artifact useful to make calculations? $\endgroup$– JackICommented Dec 8, 2017 at 17:34
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1$\begingroup$ I don't think this is correct in the case of nonabelian gauge quantum field theory; see my answer. $\endgroup$– tparkerCommented Dec 8, 2017 at 17:55
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$\begingroup$ @tparker OP is asking explicitly about electromagnetism, which is immune from any nonabelian subtleties. $\endgroup$– Emilio PisantyCommented Dec 8, 2017 at 18:06
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$\begingroup$ @EmilioPisanty Yes, but Qmechanic's original answer didn't have that caveat, and so ran the risk of being interpreted as applying to all gauge theories, including nonabelian. $\endgroup$– tparkerCommented Dec 9, 2017 at 16:01
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$\begingroup$ @Qmechanic Doesn't the restriction that you state in your first footnote make your updated answer vacuous? You're now just saying that for the class of gauge theories for which gauge transformations are unphysical, gauge transformations are unphysical. This is true but tautological. $\endgroup$– tparkerCommented Dec 9, 2017 at 16:08
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