Spatial rotation
= Spatial rotation
A spatial rotation acts by $\mathbf x\mapsto R\mathbf x$, where $R\in SO(3)$ satisfies $R^TR=I$ and $\det R=+1$. Orthogonality preserves distances and angles; the positive <determinant> excludes reflections. In <de Sitter> flat slicing it leaves <conformal time> fixed. A rotationally invariant scalar <two-point function> in a translation-invariant state depends only on the magnitude of its <momentum>.