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Hilbert Space Representations of Generalized Canonical Commutation Relations

Hilbert Space Representations of Generalized Canonical Commutation Relations

We consider Hilbert space representations of a generalization of canonical commutation relations <svg style="vertical-align:-5.76988pt;width:300.86249px;" id="M1" height="19.375" version="1.1" viewBox="0 0 300.86249 19.375" width="300.86249" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(.017,-0,0,-.017,.062,12.138)"><path id="x28" d="M300 -147l-18 -23q-106 71 -159 185.5t-53 254.5v1q0 139 53 252.5t159 186.5l18 -24q-74 -62 -115.5 -173.5t-41.5 -242.5q0 -130 41.5 -242.5t115.5 -174.5z" /></g><g transform="matrix(.017,-0,0,-.017,5.944,12.138)"><path id="x43" …