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$\begingroup$ Nice construction! In effect, it boils down to introducing a extra field $\chi$ which transforms as $\chi\to\chi-\theta_1-i\theta_2$, and replacing $\psi^\dagger i\partial_t\psi$ with $\frac i2[(\psi^\dagger+\chi^\dagger)\partial_t\psi-\partial_t\psi^\dagger(\psi+\chi)]$ and subsequently ordinary derivatives with covariant ones. I'm not sure if this is what I want though, since even after setting $A=0$, this theory has a different global symmetry than the theory I started with. Thanks anyway, you made me formulate more precisely what I'm looking for! $\endgroup$
– Tomáš Brauner
Commented Apr 17, 2013 at 13:02

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