A geometric construction of representations of the Berezin-Toeplitz quantization

29 Jan 2020  ·  Kwokwai Chan, Naichung Conan Leung, Qin Li ·

For a K\"ahler manifold $X$ equipped with a prequantum line bundle $L$, we give a geometric construction of a family of representations of the Berezin-Toeplitz deformation quantization algebra $(C^\infty(X)[[\hbar]],\star_{BT})$ parametrized by points $z_0 \in X$. The key idea is to use peak sections to suitably localize the Hilbert spaces $H^{0}\left( X,L^{\otimes m}\right) $ around $z_{0}$ in the large volume limit...

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Quantum Algebra High Energy Physics - Theory Differential Geometry 53D50, 53D55