Dispersion Operators Algebra and Linear Canonical Transformations

This work intends to present a study on relations between a Lie algebra called dispersion operators algebra, linear canonical transformation and a phase space representation of quantum mechanics that we have introduced and studied in previous works. The paper begins with a brief recall of our previous works followed by the description of the dispersion operators algebra which is performed in the framework of the phase space representation. Then, linear canonical transformations are introduced and linked with this algebra. A multidimensional generalization of the obtained results is given.

q-DERIVATION, SINE ALGEBRA AND Ut(sl(2))

We review the q-pseudo-differential operators algebra(q-ψ DO ) and some of its properties. Based on the fact that w∞ and U t( sl (2)) can be constructed from the trigonometric sine algebra (F.F.Z. algebra), we propose the embedding of w∞ and U t( sl (2)) in (q-ψ DO ). The correspondence with 2-D fractional supersymmetry algebra is examined.