b -辛环流形的Bohr-Sommerfeld量化

IF 0.5 4区数学 Q3 MATHEMATICS

Pure and Applied Mathematics Quarterly Pub Date : 2023-11-20 DOI:10.4310/pamq.2023.v19.n4.a15

Pau Mir, Eva Miranda, Jonathan Weitsman

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引用次数: 1

摘要

我们引入了双辛环流形的bor - sommerfeld量子化，并证明了它与$\href{ https://mathscinet.ams.org/mathscinet/relay-station?mr=3804693}{[\textrm{GMW18b}]}$的形式几何量子化相吻合。特别地，我们证明了它的维数是由环面作用于流形的矩多面体上的积分点的带符号计数给出的。

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Bohr–Sommerfeld quantization of $b$-symplectic toric manifolds

We introduce a Bohr–Sommerfeld quantization for bsymplectic toric manifolds and show that it coincides with the formal geometric quantization of $\href{ https://mathscinet.ams.org/mathscinet/relay-station?mr=3804693}{[\textrm{GMW18b}]}$. In particular, we prove that its dimension is given by a signed count of the integral points in the moment polytope of the torus action on the manifold.

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来源期刊

Pure and Applied Mathematics Quarterly 数学-数学

CiteScore

0.90

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Publishes high-quality, original papers on all fields of mathematics. To facilitate fruitful interchanges between mathematicians from different regions and specialties, and to effectively disseminate new breakthroughs in mathematics, the journal welcomes well-written submissions from all significant areas of mathematics. The editors are committed to promoting the highest quality of mathematical scholarship.