I have the Lagrangian \[L=-\partial_{\mu}\phi^{I}\partial^{\mu}\phi^{I}/2-m^{2}\phi^{I}\phi^{I}/2\]where I=1,2,3 and I want to find 3 independent infinitesimal transformations that leave the action invariant. One of them is a SO(3) infinitesimal rotation by \(\delta\theta, \phi->\phi'=\phi+\delta\theta\epsilon_{abc}n_{b}\phi_{c}\). Also, the lagrangian is invariant when I change the sign of the fields but I suppose that it is not an infinitesimal transformation. If I had compex fields I would have a U(1) symmetry but this doesn't work here. Any help or hint?