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$\begingroup$ Thanks a lot, this is very helpful! I still have to check how (and whether) this works in the non-Abelian case, but I have already learned quite something from you :) $\endgroup$
– Tomáš Brauner
Commented Apr 17, 2013 at 9:04
$\begingroup$ I updated the answer. $\endgroup$
– Qmechanic ♦
Commented Apr 17, 2013 at 16:22
$\begingroup$ This is again very instructive, thanks! So to summarize this example, the free Schrödinger field theory has a global ISO(2) symmetry (phase rotations plus two translations in the plane of complex $\psi$). Any of the three one-parametric Abelian subgroups can be gauged, but this breaks the remaining global symmetry. Two whole ISO(2) group, or even the normal subgroup of translations, cannot be gauged. It's good to see this so explicitly. $\endgroup$
– Tomáš Brauner
Commented Apr 18, 2013 at 8:13

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