Friday 6 May 2022, 16:00 – 17:00, M314
We start with a compact Kahler manifold that one can consider as a phase space of a classical dynamical system. We define the Berezin quantization of manifolds as a family of some special Toeplitz operators. We introduce the quantum state associated with an arbitrary submanifold of a compact Kahler manifold and see that if the submanifold is a point, its quantization is a pure quantum state, and otherwise, it is a mixed state in the semi-classical limit. We define some quantum mechanical concepts such as fidelity as a measure of overlap between a pair of quantum states and see that for two intersecting Lagrangian submanifolds, fidelity can detect the transverse intersection.
Ghazaleh Asghari (University of Reading, England)