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Physical polarization vectors are unchanged under a gauge transformation ##\epsilon + a\cdot{p}=\epsilon##, where ##a## is some arbitrary constant.

1. Why are

*physical*polarization vectors transverse?

2. Why is ##p\cdot{\epsilon}=0## the condition for the transverseness of ##\epsilon##?

2. How is ##\epsilon + a\cdot{p}=\epsilon## a gauge transformation? The gauge transformations I know are of the form ##A_{\mu}\rightarrow A_{\mu}+\partial_{\mu}\Lambda##.