Weak commutation relations of unbounded operators: Nonlinear extensions

Abstract

We continue our analysis of the consequences of the commutation relation [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 H, where the operators act. We also consider what we call, adopting a physical terminology, a nonlinear extension of the above commutation relations. C