Applications of Lie algebraic and phase space methods in quantum physics

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Phase space methods in quantum mechanics have in common the objective of mapping quantum mechanical operators, defined in an abstract Hilbert space, to complex-valued functions in a classical phase space appropriate for the system under consideration. This proposal deals with applications of phase space methods to quantum systems with higher symmetries. The proposed applications include the extension of results already available for SU(3) to systems with SU(n) (and other) symmetries, a study of short time semiclassical dynamics of such systems focusing on squeezing as a short time effect, an investigation of so-called correspondence rules with possible applications to relaxation, and an investigation of phase operators for systems with higher symmetries using phase space methods as a starting point. The results of this work will be of use to physicists - theorists and experimentalists - in quantum optics with an interest in a better understanding some nonclassical properties of quantum states.