Spatial rotation

A spatial rotation acts by $\mathbf{x}\mapsto R\mathbf{x}$, where $R\in SO(3)$ satisfies $R^{T}R=I$ 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.