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Different gauges lead to different interpretations of the theory:
For more on problems with the unitary gauge, see: Ambiguities and breakdown configurations of the unitary gauge by C. Montonen, G. ’t Hooft (1981) Nucl. Phys. B190 and M.N. Chernodub, L.D. Faddeev, A.J. Niemi (2008) JHEP 12, 014 (http://arxiv.org/abs/0804.1544).455.