I'm new to quantum mechanics, but not quite as new to linear algebra and operator theory, and trying to understand the nature of observations from a mathematical perspective. Consider a two-dimensional Hilbert space with an orthonormal basis $|0\rangle$, $|1\rangle$. Define the Hermitian operator...

It is known that flat manifolds can be characterized as follows If a pseudo-Riemannian manifold $M$ of signature $(s,t)$ has zero Riemann curvature tensor everywhere on $M$, then the manifold is locally isometric to $\mathbb{R}^{s,t}$. My question is this $-$ what other properties should a pseu...