Weak commutation relations of unbounded operators: Nonlinear extensions

Abstract

We continue our analysis of the consequences of the commutation relation \documentclass[12pt]{minimal}\begin{document}$[S, T]\break = {\bb 1}$\end{document}[S,T]=1, where S and T are two closable unbounded operators. The weak sense of this commutator is given in terms of the inner product of the Hilbert space \documentclass[12pt]{minimal}\begin{document}${\mathcal {H}},$\end{document}H, where the operators act. We also consider what we call, adopting a physical terminology, a nonlinear extension of the above commutation relations.