There is a simple fact that we can change our point of view and that physical laws should remain the same, id est, outcomes of our experiments should be the same no matter from which frame of reference we are observing. So, there is a physical state that changes under the change of our point of view and there is a new wave function which describes it. Should there be a representation of this transformation which takes the old wave function into new one? Is there any proof of such a claim? Should there always be transformation of wave function for every transformation of the physical system? Space-time coordinates are transformed of course, but what about the state itself? Is there any proof of this?
Answer
By Wigner's theorem every symmetry is represented as a unitary or anti-unitary operator upon the Hilbert space of states.
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