Deformation quantization of compact Kähler manifolds via Berezin-Toeplitz operators

Details Deformation quantization of compact Kähler manifolds via Berezin-Toeplitz operators Deformation quantization of compact Kähler manifolds via Berezin-Toeplitz operators

1996-11-19

arxiv.org/abs/q-alg/9611022v1

Physics

Mathematical Physics

6 pages, Latexe

Scientific paper

This talk reports on results on the deformation quantization (star products) and on approximative operator representations for quantizable compact K"ahler manifolds obtained via Berezin-Toeplitz operators. After choosing a holomorphic quantum line bundle the Berezin-Toeplitz operator associated to a differentiable function on the manifold is the operator defined by multiplying global holomorphic sections of the line bundle with this function and projecting the differentiable section back to the subspace of holomorphic sections. The results were obtained in (respectively based on) joint work with M. Bordemann and E. Meinrenken. (Talk at the XXI Int. Coll. on Group Theoretical Methods in Physics, 15-20 July, Goslar, Germany)

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