I have been following the proof of the Stone's theorem on one-parameter unitary groups.
The question is if the current list of self-adjoint operators used in quantum mechanics, including position, momentum, spin operators, is exhaustive or not?
Put it another way, can we say that there is no other one-parameter unitary groups, that can give us yet new self-adjoint operators, in addition to position, momentum, and spin, and therefore new observables?
I need to know if there is a classification theorem on one parameter unitary groups.
Do we know now that there is no other such one parameter unitary group that if exists at all then its generator will give us some yet unknown new observable in quantum theory?