Semiclassics for Quantum Systems with Internal Degrees of Freedom: The Semiclassical Correspondence Generalized - Softcover

Inhaltsangabe

We study semiclassical properties of quantum systemswith internal degrees of freedom. Whiletranslational degrees of freedom are described ascoordinates on the cotangent bundle of aconfiguration manifold, the internal ones find theirclassical description on more general symplecticmanifolds. The quantum space forthe translational degrees of freedom, squareintegrable functions on the configuration space, hasto be "tensored" with the representation space forthe internal ones. Consequently, quantum observablesare operators that take values in the endomorphismsof the representation space for internal degrees of freedom. One part of this work is concerned with the generalization of semiclassical techniques to the non-scalar setting. In particular, we study the semiclassical time evolution of observables and we prove a generalization of Egorov's Theorem and asemiclassical limit formula of Szegö-type. Weemploy a quantization scheme for the internaldegrees of freedom which enables us to map theirquantum character to a classical model and thusobtain a classical description for both thetranslational and internal degrees of freedom.

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