algebraic quantum field theory (perturbative, on curved spacetimes, homotopical)
quantum mechanical system, quantum probability
interacting field quantization
In quantum mechanics, a quasi-state on an algebra of observables is a function that is required to satisfy the axioms of a genuine state (linearity and positivity) only on the poset of commutative subalgebras of .
While therefore the condition on quasi-states is much weaker than that for states, Gleason's theorem asserts that if for , then all quasi-states are in fact already genuine quantum states.
Notice that a quasi-state is naturally regarded as an actual state, but internal to the ringed topos over the poset of commutative subalgebras of – the “Bohr topos”. Therefore Gleason's theorem is one of the motivations for regarding this ringed topos as the quantum phase space (“Bohrification”.) The other is the Kochen-Specker theorem.
Last revised on February 8, 2020 at 10:38:34. See the history of this page for a list of all contributions to it.