Berezin-Toeplitz量化表示的几何构造

IF 1 4区 物理与天体物理 Q3 PHYSICS, MATHEMATICAL Advances in Theoretical and Mathematical Physics Pub Date : 2020-01-29 DOI:10.4310/ATMP.2022.v26.n1.a1
Kwokwai Chan, N. Leung, Qin Li
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引用次数: 7

摘要

对于具有前量子线束$L$的Kähler流形$X$,我们给出了由点$z_0 \in X$参数化的Berezin-Toeplitz变形量化代数$(C^\infty(X)[[\hbar]],\star_{BT})$的一族表示的几何构造。关键思想是使用峰值截面来适当地定位$z_{0}$周围的希尔伯特空间$H^{0}\left( X,L^{\otimes m}\right) $。
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A geometric construction of representations of the Berezin–Toeplitz quantization
For a K\"ahler manifold $X$ equipped with a prequantum line bundle $L$, we give a geometric construction of a family of representations of the Berezin-Toeplitz deformation quantization algebra $(C^\infty(X)[[\hbar]],\star_{BT})$ parametrized by points $z_0 \in X$. The key idea is to use peak sections to suitably localize the Hilbert spaces $H^{0}\left( X,L^{\otimes m}\right) $ around $z_{0}$.
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来源期刊
Advances in Theoretical and Mathematical Physics
Advances in Theoretical and Mathematical Physics 物理-物理:粒子与场物理
CiteScore
2.20
自引率
6.70%
发文量
0
审稿时长
>12 weeks
期刊介绍: Advances in Theoretical and Mathematical Physics is a bimonthly publication of the International Press, publishing papers on all areas in which theoretical physics and mathematics interact with each other.
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