Real scalar triplet ($\Phi =({\Phi }_1,{\Phi }_2,{\Phi }_3{)}^T$)

A real scalar triplet groups three real scalar components into a vector under SO(3). Equivalently it is the three-dimensional Adjoint representation of SU(2), whose center acts trivially. Its rotationally invariant quadratic and quartic potentials depend on $\Phi \cdot \Phi$. A nonzero vacuum direction leaves rotations around that direction unbroken.

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.