| Condition of Prequantization to Two—Dimensional Manifolds with Boundary |
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| 引用本文： | SHAOMing－Xue ZHUZHONG－Yuan.Condition of Prequantization to Two—Dimensional Manifolds with Boundary[J].理论物理通讯,2001,35(3):263-266. |
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| 作者姓名： | SHAOMing－Xue ZHUZHONG－Yuan |
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| 作者单位： | [1]DepartmentofPhysics,JishouUniversity,Jishou416000,HunanProvince,China;DepartmentofPhysics,BeijingNormalUniversity,Beijing100875,China [2]InstituteofTheoreticalPhysics,AcademiaSInica,P.O.Bo |
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| 摘 要： | The Weil‘s integrality condition of prequantization is generalized to two-dimensional phase space with boundaries.It is shown that in the prequantization condition a term related to the symplectic potential on the boundary appears.The necessity of the generalized condition is proved by analyzing the isolated singularities of the Hermitian bundle while the sufficiency of the condition is proved via geometric construction on the space of equivalence class.
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| 关 键 词： | 经典力学 几何量子化 二维流形 |
| 收稿时间： | 2000-08-29 |
Condition of Prequantization
to Two-Dimensional Manifolds with Boundary |
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| SHAO Ming-Xue,ZHU Zhong-Yuan.Condition of Prequantization
to Two-Dimensional Manifolds with Boundary[J].Communications in Theoretical Physics,2001,35(3):263-266. |
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| Authors: | SHAO Ming-Xue ZHU Zhong-Yuan |
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| Institution: | 1. Institute of Theoretical Physics, Academia Sinica, P.O. Box 2735, Beijing 100080, China
;2. Department of Physics, Jishou University, Jishou 416000, Hunan
Province, China
;3. Department of Physics, Beijing Normal University,
Beijing 100875, China |
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| Abstract: | The Weil's integrality condition of prequantization is generalized
to two-dimensional phase space with boundaries. It is shown that in the
prequantization condition a term related to the symplectic potential on the boundary appears. The necessity of the generalized condition is proved by
analyzing the isolated singularities of the Hermitian bundle while the
sufficiency of the condition is proved via geometric construction on the
space of equivalence class. |
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| Keywords: | Weil's condition boundary prequantization |
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