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Article Dans Une Revue Communications in Mathematical Physics Année : 2003

Berezin-Toeplitz Operators, a Semi-Classical Approach

Résumé

This article is devoted to the Toeplitz Operators in the context of the geometric quantization. We propose an ansatz for their Schwartz kernel. From this, we deduce the main known properties of the principal symbol of these operators and obtain new results : we define their covariant and contravariant symbols, which are full symbols, and compute the product of these symbols in terms of the Kähler metric. This gives canonical star products on the Kählerian manifolds. This ansatz is also useful to introduce the notion of microsupport.

Dates et versions

hal-04014269 , version 1 (03-03-2023)

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Laurent Charles. Berezin-Toeplitz Operators, a Semi-Classical Approach. Communications in Mathematical Physics, 2003, 239 (1-2), pp.1-28. ⟨10.1007/s00220-003-0882-9⟩. ⟨hal-04014269⟩
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