Global phase symmetry
= Global phase symmetry
{title2=$\varphi_j\mapsto e^{-iq_j\alpha}\varphi_j$}
An internal <circle group> action with spacetime-independent parameter $\alpha$. For canonical <complex scalar fields>, <Noether's theorem> gives $j^\mu=i\sum_jq_j\varphi_j^\dagger\overleftrightarrow{\partial^\mu}\varphi_j$. The <Noether charge> of the <particle> annihilated by $\varphi_j$ is $q_j$, and its <antiparticle> has charge $-q_j$.