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A categorification of the boson oscillator
  • ISSN号：0253-6102
  • 期刊名称：Commun. Theor. Phys.
  • 时间：2012.1.1
  • 页码：34-40
  • 分类：O431[机械工程—光学工程;理学—光学;理学—物理] TN752[电子电信—电路与系统]
  • 作者机构：[1]School of Mathematical Sciences, Capital Normal University, Beijing 100048, China
  • 相关基金：Supported by National Natural Science Foundation of China under Grant Nos. 10975102, 10871135, 11031005, 11075014Acknowledgements The authors gratefully acknowledge the support of the Morningside Center of Mathematics and Professor Wang Shi-Kun. The first author would like to thank Gao XiuHong, Wang Xiao-Hong and especially Wang Na for useful discussions.
  • 相关项目：广义纠缠相干态表象及其应用的研究
作者： B-S Lin|K Wu|
关键词： 振荡器, FOCK态, 量子力学, 玻色子, 分类, 产品, 定义, 内积, categorification, Boson oscillator, Fock state, Heisenberg algebra
中文摘要：

在这份报纸，我们调查对波色子振荡器的范畴的描述。基于 Khovanov 构造的范畴，我们介绍 Fock 状态和这些状态的相应内部产品的 categorification。我们发现有 Fock 状态的内部产品的二个不同范畴的定义。这二个定义与对方一致，并且 decategorification 结果也在常规量力学与那些与一致。我们也发现有联系到状态的内部产品的 2-morphisms 的一些有趣的性质。

英文摘要：

In this paper, we investigate the categorical description of the boson oscillator. Based on the categories constructed by Khovanov, we introduce a categorification of the Fock states and the corresponding inner product of these states. We find that there are two different categorical definitions of the inner product of the Fock states. These two definitions are consistent with each other, and the decategorification results also coincide with those in conventional quantum mechanics. We also find that there are some interesting properties of the 2-morphisms which relate to the inner product of the states.

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期刊信息
  • 《理论物理通讯：英文版》
  • 中国科技核心期刊
  • 主管单位:中国科学院
  • 主办单位:中科院理论物理所 中国物理学会
  • 主编：孙昌浦
  • 地址：北京2735邮政信箱 中国科学院理论物理研究所编辑部
  • 邮编：100190
  • 邮箱：ctp@itp.ac.cn
  • 电话：010-62551495 62541813 62550630
  • 国际标准刊号：ISSN：0253-6102
  • 国内统一刊号：ISSN：11-2592/O3
  • 邮发代号:
  • 获奖情况:
  • 首届国家期刊奖,中国科学院优秀期刊特别奖,国家期刊奖百种重点期刊,中国期刊方阵“双高”期刊
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  • 被引量:342