We can construct a Hermitian operator O in the following general way:
- find a complete set of projectors Pλ which commute,
- assign to each projector a unique real number λ∈R.
By this, each projector defines an eigenspace of the operator O, and the corresponding eigenvalues are the real numbers λ. In the particular case in which the eigenvalues are non-degenerate, the operator O has the form
O=∑λλ|λ⟩⟨λ|
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?
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