I want to study a QFT, given by an action $S$ which is defined in $(2+1)$ dimensions, i.e. $$ S=\int d^3x \mathcal{L}[\phi,\,\partial\phi]. $$ This QFT is invariant under rotations, i.e. in radial coordinates $r=\sqrt{x^2+y^2}$ and $\theta=\tan^{-1}(y/x)$, the action is invariant under a transfor...