Understanding Reference Frames in Quantum Mechanics

[mhazelm]

This might be a dumb question to ask, but does anyone ever worry about reference frames in QM? I'm just starting my first course and don't know much yet, but it seems like if we can consider operators to be vector fields (reference to my previous post) then we might have to worry about groups of transformations that preserve the structure of our vector space versus those that do not.

Am I right in thinking that we can interpret physical information about our reference frame from the flows of a vector field?

 

[waht]

Yea, the vector space is spanned by eigenfunctions. And you can do a change of basis from one to another.

 

[Fredrik]

Your question made no sense to me at first, and I'm still not sure what you're asking. In quantum field theory, creation and annihilation operators (operators that change the number of particles in a state) are combined into operator-valued scalar fields, tensor fields or spinor fields. A vector field is a special kind of tensor field. But you don't seem to be talking about those at all.

The other thread suggests that you're talking about vector fields on Lie groups, not on spacetime. So why are you concerned about reference frames? It sounds like you're worried that if you e.g. use something different than your usual Euler angles to label rotations, rotation operators will act on a completely different Hilbert space? That's definitely not the case.

Maybe you should explain what you're really asking.