CRM: Centro De Giorgi
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Regular and Stochastic Behaviour in Dynamical Systems

Some relationship between classical and quantum dynamics

speaker: Frédéric Faure (Université de Grenoble Alpes)

abstract: In geometric quantization (Kostant Souriau 70' ), we start from a Hamiltonian dynamical system. We consider (1) its contact R-extension which is a naturally defined dynamical system (called pre-quantum). The step (2) called quantization consists in projecting it on the quotient space by an arbitrary non-invariant Lagrangian integrable distribution (called polarization). This construction gives the Schrodinger equation in physics but it is not unique. In this talk, it will be shown and discussed that for an Anosov geodesic flow, the pre-quantum dynamics already naturally and dynamically defines a quantization where the polarization corresponds to the stable invariant distribution. Work in collaboration with Masato Tsujii.

Thu 8 Jun, 10:30 - 11:30, Aula Dini
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