We can construct a Hermitian operator $O$ in the following general way:

- find a complete set of projectors $P_\lambda$ which commute,
- assign to each projector a unique real number $\lambda\in\mathbb R$.

By this, each projector defines an eigenspace of the operator $O$, and the corresponding eigenvalues are the real numbers $\lambda$. In the particular case in which the eigenvalues are non-degenerate, the operator $O$ has the form
$$O=\sum_\lambda\lambda|\lambda\rangle\langle\lambda|$$

**Question:** what restrictions which prevent $O$ from being an observable are known?

For example, we can't admit as observables the Hermitian operators having as eigenstates superpositions forbidden by the superselection rules.

**a)** Where can I find an exhaustive list of the superselection rules?

**b)** Are there other rules?

**Update:**

**c)** Is the particular case when the Hilbert space is the tensor product of two Hilbert spaces (representing two quantum systems), special from this viewpoint?

This post has been migrated from (A51.SE)