What direction is the angular momentum of right hand polarized light points to? Is it vertical to its propagating direction? I want to recognize this in quantum theory.
A “right-handed” photon has its spin parallel to its linear momentum; a “left-handed” photon’s spin is antiparallel to its linear momentum. The psuedoscalar product $\vec\sigma\cdot\vec p$ is sometimes called the “helicity.”
Beware that “right-circular polarized” light is made of left-handed photons, and vice-versa (because history is cruel). This is demonstrated conclusively in my favorite classic physics paper: Richard Beth, Mechanical detection and measurement of the angular momentum of Light, Physical Review 50 115 (1936). See this answer for a brief summary of Beth’s experiment.