SO(3) Noether current of a real scalar triplet ($J_a^{\mu }={ϵ}_{abc}({\partial }^{\mu }{\varphi }_b){\varphi }_c$)

A real triplet with a rotationally invariant common mass term has three conserved internal currents. With the displayed sign convention, the current for $\delta \mathbf{\varphi }=\theta \mathbf{n}\times \mathbf{\varphi }$ is the negative of the conventional canonical current contracted with $\mathbf{n}$. Overall current sign does not affect conservation. Integrated charges require convergent integrals and vanishing net boundary flux; a local continuity equation alone does not guarantee conservation in an open region.