ORDERING RELATIONS FOR Q-BOSON OPERATORS, CONTINUED-FRACTION TECHNIQUES AND THE Q-CBH ENIGMA

Ordering properties of boson operators have been very extensively stud ied, and q-analogues of many of the relevant techniques have been deri ved. These relations have far reaching physical applications and, at t he same time, provide a rich and interesting source of combinatorial i dentities and of their g-analogues. An interesting exception involves the transformation from symmetric to normal ordering, which, for conve ntional boson operators, can most simply be effected using a special c ase of the Campbell-Baker-Hausdorff (CBH) formula. To circumvent the l ack of a suitable q-analogue of the CBH formula, two alternative proce dures are proposed, based on a recurrence relation and on a double con tinued fraction, respectively. These procedures enrich the repertoire of techniques available in this field. For conventional bosons they re sult in an expression that coincides with that derived using the CBH f ormula.