前量子系统的达尔布定理、莫泽定理和温斯坦定理及其在几何量子化中的应用

IF 1.6 3区数学 Q1 MATHEMATICS

Journal of Geometry and Physics Pub Date : 2024-08-22 DOI:10.1016/j.geomphys.2024.105298

Eva Miranda , Jonathan Weitsman

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引用次数: 0

摘要

我们为前量子系统建立了达尔布（Darboux）、莫泽（Moser）和温斯坦（Weinstein）定理的类似物。我们证明，流形上的两个前量子系统具有消失的第一同调，它们的交映形式定义了相同的同调类，并且在该类内彼此同构，它们之间只有交映变换和量规变换的区别。作为应用，我们证明了在具有微不足道的第一同调的流形上的前量子系统的玻尔-索默费尔德量子化与连接的选择无关。

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Darboux, Moser and Weinstein theorems for prequantum systems and applications to geometric quantization

We establish analogs of the Darboux, Moser and Weinstein theorems for prequantum systems. We show that two prequantum systems on a manifold with vanishing first cohomology, with symplectic forms defining the same cohomology class and homotopic to each other within that class, differ only by a symplectomorphism and a gauge transformation. As an application, we show that the Bohr-Sommerfeld quantization of a prequantum system on a manifold with trivial first cohomology is independent of the choice of the connection.

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来源期刊

Journal of Geometry and Physics 物理-物理：数学物理

CiteScore

2.90

自引率

6.70%

发文量

205

审稿时长

64 days

期刊介绍： The Journal of Geometry and Physics is an International Journal in Mathematical Physics. The Journal stimulates the interaction between geometry and physics by publishing primary research, feature and review articles which are of common interest to practitioners in both fields. The Journal of Geometry and Physics now also accepts Letters, allowing for rapid dissemination of outstanding results in the field of geometry and physics. Letters should not exceed a maximum of five printed journal pages (or contain a maximum of 5000 words) and should contain novel, cutting edge results that are of broad interest to the mathematical physics community. Only Letters which are expected to make a significant addition to the literature in the field will be considered. The Journal covers the following areas of research: Methods of: • Algebraic and Differential Topology • Algebraic Geometry • Real and Complex Differential Geometry • Riemannian Manifolds • Symplectic Geometry • Global Analysis, Analysis on Manifolds • Geometric Theory of Differential Equations • Geometric Control Theory • Lie Groups and Lie Algebras • Supermanifolds and Supergroups • Discrete Geometry • Spinors and Twistors Applications to: • Strings and Superstrings • Noncommutative Topology and Geometry • Quantum Groups • Geometric Methods in Statistics and Probability • Geometry Approaches to Thermodynamics • Classical and Quantum Dynamical Systems • Classical and Quantum Integrable Systems • Classical and Quantum Mechanics • Classical and Quantum Field Theory • General Relativity • Quantum Information • Quantum Gravity