Internal rotation symmetry of two real scalar fields

For two free real scalar fields, the internal rotation $\delta {\varphi }_1=\theta {\varphi }_2$, $\delta {\varphi }_2=-\theta {\varphi }_1$ is a symmetry precisely when their squared masses agree. Its Noether current is $j^{\mu }={\varphi }_2{\partial }^{\mu }{\varphi }_1-{\varphi }_1{\partial }^{\mu }{\varphi }_2$. Without mass degeneracy, ${\partial }_{\mu }{j}^{\mu }=(m_2^2-m_1^2){\varphi }_1{\varphi }_2$.