Complex Lagrangian subspaces and representations of the canonical commutation relations

Abstract: Complex Lagrangian subspaces were introduced as polarizations on symplectic manifolds in geometric quantization. We will look at their role in the linear geometry more carefully. A transverse pair of complex Lagrangian subspaces parametrizes representations of the canonical commutation relations and this brings together some different perspectives from which the representations were studied. I will suggest how this result can be interpreted using concepts from geometry and very little concepts from physics.

differential geometrydynamical systemsgeometric topologysymplectic geometry

Audience: researchers in the topic

Geometry and Dynamics seminar

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