Spinorial Structure of $O(3)$ and Application to Dark Matter

Teruyuki Kitabayashi, Masaki Yasuè

An $O(3)$ spinor, $\Phi$, as a doublet denoted by $2_D$ consists of an $SO(3)$ spinor, $\varphi$, and its complex conjugate, ${\varphi }^{\ast }$, which form $\Phi ={\left(\varphi ,{\varphi }^{\ast }\right)}^T$ to be ide…