Four possible definitions of the commutation relation [S, T] = 11 of two closableunbounded operators S, T are compared. The weak sense of this commutator isgiven in terms of the inner product of the Hilbert space H where the operators act.Some consequences on the existence of eigenvectors of two numberlike operators arederived and the partial O*-algebra generated by S, T is studied. Some applicationsare also considered.
|Number of pages||14|
|Journal||Journal of Mathematical Physics|
|Publication status||Published - 2011|
All Science Journal Classification (ASJC) codes
- Statistical and Nonlinear Physics
- Mathematical Physics