Heisenberg evolution of quantum observables represented by unbounded operators

Werner Timmermann

Gerd Laßner

Andreas Andersson

We describe rigorous quantum measurement theory in the Heisenberg picture by applying operator deformation techniques previously used in noncommutative quantum field theory. This enables the conventional observables (represented by unbounded operators) to play a role also in the more general setting.

Giuseppina Epifanio, Todor S. Todorov, Camillo Trapanı

The notion of completeness of a set 𝒮 of compatible observables represented by maximal symmetric operators is discussed directly in terms of unbounded operators. In contrast with what happens for self-adjoint observables, the present framework forces us to involve some partial algebraic structures such as the partial GW*-algebra generated by 𝒮. In this way the previous approaches based on von Neumann algebras and on O*-algebras are generalized.

Sebastián Fortín, Manuel Gadella, Federico Holik +1 more

Rafael de la Madrid

It is well known that the unboundedness of operators in Hilbert space entails domain troubles. It is also well known that most domain troubles can be surmounted by extending the Hilbert space to a rigged Hilbert space. In this note, we point out another of such troubles, namely the correspondence between the Schrodinger and the Heisenberg pictures for unbounded operators, and sketch the solution of this problem within the rigged Hilbert space.