ANGULAR MOMENTUM-ANGLE COMMUTATION RELATIONS AND MINIMUM UNCERTAINTY STATES

摘要

We extend the canonical commutation relations (CCR) in quantum mechanics to the case where appropriate dynamical variables are angular momenta and angles. It is found that projection operators of the resultant Weil algebra provide us with a new and powerful way of characterizing minimum uncut states, including those obtained by Caruthers and Nieto. The uniqueness theorem of Schrodinger representation remains valid for extended CCR in a simple case. Finally, a wide range of applicability of our method is suggested.