Contact quantization: quantum mechanics = parallel transport

I will discuss some recent work with A. Waldron in which we reformulate quantum mechanics as the problem of finding an appropriate flat connection on a Hilbert bundle over a contact manifold. Quantum dynamics is then governed by the parallel transport associated with this flat connection. Our main result is a proof of local unitary equivalence for a broad class of quantum dynamical systems. This equivalence can be exploited to find simple, if somewhat formal relations between between the correlators of physically different quantum mechanical systems.

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Jeudi, Août 23, 2018 - 14:30 to 16:00
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