# Definition *Internal Symmetries* are internal [[degree of freedom|degrees of freedom]] of a quantum mechanical system. They are unrelated to the spatial degrees of freedom, and manifest as additional [[Hilbert Space|Hilbert spaces]] $\mathcal{H}_{\text{internal}}$ that must be [[tensor product|tensor producted]] with $L^2(\mathbb{R}^3)$ (in 3-spatial dimensions). The symmetries acting on $\mathcal{H}_{\text{internal}}$ are unrelated to the symmetries of spacetime, and examples include $SU(2)$ [[Physics/Spin]], $SU(2)$ [[Isospin|isospin]], $SU(3)$ [[Color|color]], and $SU(3)$ [[flavor|flavor]].