In the first lecture, I will present the general problem of quantization. Starting from a classical phase space (symplectic manifold), how to define a quantum space (Hilbert space) and transform Hamiltonians into linear operators? I will give details about the left, right, and Weyl quantization on ${\mathbb R}^{2n}$.

References

• Terry Tao blog on Weyl quantization
• S. Vũ Ngọc, Symplectic Techniques for Semiclassical Completely Integrable Systems, 2005
• S. Vũ Ngọc, Systèmes intégrables semi-classiques: du local au global, 2006
• D. Sepe and S. Vũ Ngọc, Integrable systems, symmetries, and quantization, 2017