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In Weinberg's QFT book(section 2.2), he said after proved the generator of the symmetry group is Hermitian and can be a candidate for an observable:

Indeed, most(and perhaps all) of the observables of physics, such as angular momentum or momentum, arise in this way from symmetry transformations.

My questions:

1. Does the observable here mean at least in principle, we can measure it in experment?

2. Does generator of any symmetry group stand for an observable? (I know a exception, SUSY grnerator seems not to be an observable. But are there other exceptions or what is the most common case?)

3. Does every observable come up this way? Or what are observables in QFT? Does it the same with observables in QM? In Dirac's book of QM he said a Hermitian operator with a complete set of eigenstates can in principle be observed in experiments. If QM and QFT are the same in this sense, then a Hermitian scalar field or a Majorana Fermion field is an observable in every space-time point. But does it true?

Thank you very much and happy new year!