My physics book (The Fundamentals of Physics) while explaining vector-ness of angular quantity (formally "Are Angular Quantities Vectors?") states that angular velocity and angular acceleration are vectors. But the turning point comes when it talks about angular displacement and states that this ...

$g^{ab}$ is the metric tensor (Minkowski) Im trying to understand if this is true: $g^{ab}g_{ab}=?=g^{aa}g_{aa}$ Have a nice day.

Is there any way to prove $$ e^{-i\beta p}|q\rangle = |q+\beta\rangle $$ just by using these identities $$ [q,\mathcal{F}(p)]=i\hbar \mathcal{F}'(p) \;\;\;\;[q,p]=i\hbar $$ in quantum mechanics?