Ops, sorry, you're right! I was thinking for some reason about classical fields... I better know well the ordinary theory of angular momentum quantization in QM!
Ok, I'm fine with the interpretation of the position operator as the generator of translations in momentum space (in the context of QM). But what would be its physical meaning? For the momentum operator, invariance under translations is just a statement of the homogeneity of space. Is invariance...
For me, a symmetry is a coordinate transformation of the space-time labels or a redefinition of the fields such that the action doesn't change. I think the term symmetry generator is restricted however only to continuous symmetries (a Lie group of symmetries). So, the number operator is...
We know that observables correspond to hermitian operators on the Hilbert space of physical states of the system. We also know, via Wigner theorem, that for each symmetry there is a linear unitary operator (or anti-linear and anti-unitary). In the case of a continuous symmetry, that is in the...
That was helpful, thanks.
By equivalent I mean equivalent in the sense of the EP, the two observer cannot say if they are falling in a gravitational field or drifting at constant speed through empty space. Along this line of thought: Neglecting tidal forces, the falling observer crosses the...
In SR there is a whole family of so called inertial observers that are defined as those observers that move at relative constant speed with respect to one another, whose descriptions of nature are all equivalent and whose spacetime coordinate are related by Lorentz transformations i.e. those...