Singular Bohr-Sommerfeld leaves and geometric quantization.
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Word Count
22,250 words, Guess
Page Count
89 pages
Identifiers
- ISBN-100494077255
- ISBN-139780494077252
- OCLC Control Number144601445
- Open LibraryOL21302869M
Description
When geometric quantization is applied to a manifold using a real polarization which is "nice enough", a result of Sniatycki says that the quantization can be found by counting certain objects, called Bohr-Sommerfeld leaves. Subsequently, several authors have taken this as motivation for counting Bohr-Sommerfeld leaves when studying the quantization of manifolds which are less "nice".In this thesis, we examine the quantization of compact symplectic manifolds that can locally be modelled by a toric manifold, using a real polarization modelled on fibres of the moment map. We compute the results directly, and obtain a theorem similar to Sniatycki's, which gives the quantization in terms of counting Bohr-Sommerfeld leaves. However, the count does not include the Bohr-Sommerfeld leaves which are singular. Thus the quantization obtained is different from the quantization obtained using a Kaehler polarization.
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- Singular Bohr-Sommerfeld leaves and geometric quantization.
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