The structure of projection-valued states: A generalization of Wigner's theorem

A projection-valued state is defined to be a completely orthoadditive map from the projections on one Hilbert space into the projections on another Hilbert space, which preserves the unit. Any such mapping is shown to have the formP U ₁(P 1₁)U ₁ ^–1 U ₂(P 1₂)U ₂ ^–1 , whereU ₁ is unitary andU ₂ is antiunitary, generalizing Wigner's theorem on symmetry transformations. A physical interpretation is given and the relation to quantum logic is discussed.The contents of this paper are a portion of the author's dissertation at the University of Massachusetts at Amherst.