| Description |
1 online resource (v, 60 pages) : illustrations |
| Series |
Memoirs of the American Mathematical Society, 0065-9266 ; number 971 |
|
Memoirs of the American Mathematical Society ; no. 971.
|
| Contents |
Introduction -- Background -- The cylinder -- The complex plane -- Example : S2 -- The multidimensional case -- A better way to calculate cohomology -- Piecing and glueing -- Real and Kähler polarizations compared |
| Summary |
"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 paper, the author examines 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. The author computes the results directly and obtains 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 Kähler polarization."--Publisher's description |
| Notes |
"Volume 207, number 971 (first of 5 numbers)." |
| Bibliography |
Includes bibliographical references (pages 59-60) |
| Notes |
English |
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Print version record |
| Subject |
Geometric quantization.
|
|
MATHEMATICS -- Geometry -- General.
|
|
Geometric quantization
|
| Form |
Electronic book
|
| ISBN |
9781470405854 |
|
1470405857 |
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