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Semiclassical Almost Isometry
- Source :
- Letters in Mathematical Physics. 78:189-204
- Publication Year :
- 2006
- Publisher :
- Springer Science and Business Media LLC, 2006.
-
Abstract
- Let M be a complex projective manifold, and L an Hermitian ample line bundle on it. A fundamental theorem of Gang Tian, reproved and strengthened by Zelditch, implies that the Khaeler form of L can be recovered from the asymptotics of the projective embeddings associated to large tensor powers of L. More precisely, with the natural choice of metrics the projective embeddings associated to the full linear series |kL| are asymptotically symplectic, in the appropriate rescaled sense. In this article, we ask whether and how this result extends to the semiclassical setting. Specifically, we relate the Weinstein symplectic structure on a given isodrastic leaf of half-weighted Bohr-Sommerfeld Lagrangian submanifolds of M to the asymptotics of the the pull-back of the Fubini-Study form under the semiclassical projective maps constructed by Borthwick, Paul and Uribe.<br />exposition improved
- Subjects :
- Ample line bundle
Pure mathematics
isodrastic leaf
FOS: Physical sciences
Semiclassical physics
Isometry (Riemannian geometry)
Tensor (intrinsic definition)
FOS: Mathematics
Fourier integral operator
Mathematics::Symplectic Geometry
Mathematical Physics
Mathematics
Fundamental theorem
Hodge manifold
Statistical and Nonlinear Physics
Mathematical Physics (math-ph)
Bohr-Sommerfeld Lagrangian submanifold
MAT/07 - FISICA MATEMATICA
asymptotic expansions
Hermitian matrix
Manifold
Mathematics - Symplectic Geometry
BPU map
Symplectic Geometry (math.SG)
MAT/03 - GEOMETRIA
Symplectic geometry
Subjects
Details
- ISSN :
- 15730530 and 03779017
- Volume :
- 78
- Database :
- OpenAIRE
- Journal :
- Letters in Mathematical Physics
- Accession number :
- edsair.doi.dedup.....9dbd7ea9b1e16c8bcf05deb01ade6901