Physics – Mathematical Physics
Scientific paper
2011-10-29
Physics
Mathematical Physics
In press in Journal of Mathematical Physics
Scientific paper
Four possible definitions of the commutation relation $[S,T]=\Id$ of two closable unbounded operators $S,T$ are compared. The {\em weak} sense of this commutator is given in terms of the inner product of the Hilbert space $\H$ where the operators act. Some consequences on the existence of eigenvectors of two number-like operators are derived and the partial O*-algebra generated by $S,T$ is studied. Some applications are also considered.
Bagarello Fabio
Inoue Atsushi
Trapani Camillo
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