NONCLASSICAL STATES OF LIGHT AND CANONICAL-TRANSFORMATIONS

Representations of non-linear non-bijective canonical transformations in quantum mechanics are discussed. Due to the non-bijectivity the classical phase space has a Riemann sheet structure, and a family of partial isometries translating this structure into quantum mechanics is constructed. If a unitary representation is required, a new variable-the ambiguity spin-has to be introduced in order to recover bijectivity following the approach of Moshinsky and co-workers. This new degree of freedom is analysed in terms of multiboson operators. The application of this formalism to some non-classical states of light is discussed.