An important problem in geometric quantization is that of quantizing certain classes of Lagrangian submanifolds, so-called Bohr-Sommerfeld Lagrangian submanifolds, equipped with a smooth half-density. A procedure for this in the complex projective setting is, roughly speaking, to apply the Szego kernel of the quantizing line bundle to a certain induced delta function supported on the submanifold. If the quantizing line bundle L is replaced by its k-th tensor power, and k tends to infinity, the resulting quantum states u_k concentrate asymptotically on the submanifold. This note deals with the scaling asymptotics of the u_k's along the submanifold; in particular, we point out a natural factorization in the corresponding asymptotic expansion, and provide some remainder estimates

Paoletti, R. (2008). A note on scaling asymptotics for Bohr-Sommerfeld Lagrangian submanifolds. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 136(11), 4011-4017 [10.1090/S0002-9939-08-09410-0].

A note on scaling asymptotics for Bohr-Sommerfeld Lagrangian submanifolds

Paoletti, R
2008

Abstract

An important problem in geometric quantization is that of quantizing certain classes of Lagrangian submanifolds, so-called Bohr-Sommerfeld Lagrangian submanifolds, equipped with a smooth half-density. A procedure for this in the complex projective setting is, roughly speaking, to apply the Szego kernel of the quantizing line bundle to a certain induced delta function supported on the submanifold. If the quantizing line bundle L is replaced by its k-th tensor power, and k tends to infinity, the resulting quantum states u_k concentrate asymptotically on the submanifold. This note deals with the scaling asymptotics of the u_k's along the submanifold; in particular, we point out a natural factorization in the corresponding asymptotic expansion, and provide some remainder estimates
Articolo in rivista - Articolo scientifico
Lgrangian submanifold, quantization, Szego kernel, asymptotics
English
2008
136
11
4011
4017
none
Paoletti, R. (2008). A note on scaling asymptotics for Bohr-Sommerfeld Lagrangian submanifolds. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 136(11), 4011-4017 [10.1090/S0002-9939-08-09410-0].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/2208
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