2007
DOI: 10.1007/s00220-007-0291-6
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A Formal Model of Berezin-Toeplitz Quantization

Abstract: We give a new construction of symbols of the differential operators on the sections of a quantum line bundle L over a Kähler manifold M using the natural contravariant connection on L. These symbols are the functions on the tangent bundle T M polynomial on fibres. For high tensor powers of L, the asymptotics of the composition of these symbols leads to the star product of a deformation quantization with separation of variables on T M corresponding to some pseudo-Kähler structure on T M . Surprisingly, this sta… Show more

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Cited by 9 publications
(10 citation statements)
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“…The second equation in (25) can be proved similarly. The last four equations in (25) follow immediately from formulas (19) and Proposition 4.1.…”
Section: A Star Product On T M ⊕ πT Mmentioning
confidence: 99%
See 3 more Smart Citations
“…The second equation in (25) can be proved similarly. The last four equations in (25) follow immediately from formulas (19) and Proposition 4.1.…”
Section: A Star Product On T M ⊕ πT Mmentioning
confidence: 99%
“…It was shown in [19] that Ω −1 := π * T M ω −1 + Ξ −1 is also a global pseudo-Kähler form on T M. We denote by • the star product with separation of variables on the pseudo-Kähler manifold (T M, Ω −1 ) with the classifying form…”
Section: A Star Product On T M ⊕ πT Mmentioning
confidence: 99%
See 2 more Smart Citations
“…(cf. also [5,7,14,21,22,27,31] and especially the nice survey by Schlichenmaier [49] for related works on Berezin-Toeplitz quantization).…”
Section: Introductionmentioning
confidence: 99%