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A diagrammatic categorification of the fermion algebra
  • ISSN号：1674-1056
  • 期刊名称：Chinese Physics B
  • 时间：2013
  • 页码：-
  • 分类：O153.1[理学—数学;理学—基础数学] O4-09[理学—物理]
  • 作者机构：[1]Department of Mathematics, South China University of Technology, Guangzhou 510641, China, [2]School of Mathematical Sciences, Capital Normal University, Beijing 100048, China
  • 相关基金：Project supported by the National Natural Science Foundation of China （Grant Nos. 10975102, 10871135, 11031005, and 11075014）.
  • 相关项目：量子场论和弦理论中的数学问题
作者： 林冰生|王志玺|吴可|杨紫峰|
关键词： 子代数, 费米, 图解, 粒子数态, 矢量空间, 量子力学, 图形类, 类似物, categorification, fermion algebra
中文摘要：

In this paper,we study the diagrammatic categorification of the fermion algebra.We construct a graphical category corresponding to the one-dimensional(1D) fermion algebra,and we investigate the properties of this category.The categorical analogues of the Fock states are some kind of 1-morphisms in our category,and the dimension of the vector space of 2-morphisms is exactly the inner product of the corresponding Fock states.All the results in our categorical framework coincide exactly with those in normal quantum mechanics.

英文摘要：

In this paper, we study the diagrammatic categorification of the fermion algebra. We construct a graphical category corresponding to the one-dimensional （1D） fermion algebra, and we investigate the properties of this category. The categorical analogues of the Fock states are some kind of 1-morphisms in our category, and the dimension of the vector space of 2-morphisms is exactly the inner product of the corresponding Fock states. All the results in our categorical framework coincide exnetlv with those in normal quantum mechanics.

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期刊信息
  • 《中国物理B：英文版》
  • 中国科技核心期刊
  • 主管单位:中国科学院
  • 主办单位:中国物理学会和中国科学院物理研究所
  • 主编：欧阳钟灿
  • 地址：北京 中关村 中国科学院物理研究所内
  • 邮编：100080
  • 邮箱：
  • 电话：010-82649026 82649519
  • 国际标准刊号：ISSN：1674-1056
  • 国内统一刊号：ISSN：11-5639/O4
  • 邮发代号:
  • 获奖情况:
  • 国内外数据库收录:
  • 被引量:406