中国物理B ›› 2013, Vol. 22 ›› Issue (10): 100201-100201.doi: 10.1088/1674-1056/22/10/100201

• GENERAL •    下一篇

A diagrammatic categorification of the fermion algebra

林冰生a, 王志玺b, 吴可b, 杨紫峰b   

  1. a Department of Mathematics, South China University of Technology, Guangzhou 510641, China;
    b School of Mathematical Sciences, Capital Normal University, Beijing 100048, China
  • 收稿日期:2013-03-21 修回日期:2013-04-13 出版日期:2013-08-30 发布日期:2013-08-30
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant Nos. 10975102, 10871135, 11031005, and 11075014).

A diagrammatic categorification of the fermion algebra

Lin Bing-Sheng (林冰生)a, Wang Zhi-Xi (王志玺)b, Wu Ke (吴可)b, Yang Zi-Feng (杨紫峰)b   

  1. a Department of Mathematics, South China University of Technology, Guangzhou 510641, China;
    b School of Mathematical Sciences, Capital Normal University, Beijing 100048, China
  • Received:2013-03-21 Revised:2013-04-13 Online:2013-08-30 Published:2013-08-30
  • Contact: Lin Bing-Sheng E-mail:sclbs@scut.edu.cn
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant Nos. 10975102, 10871135, 11031005, and 11075014).

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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.

关键词: categorification, fermion algebra

Abstract: 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.

Key words: categorification, fermion algebra

中图分类号:  (Rings and algebras)

  • 02.10.Hh
03.65.Ca (Formalism) 03.65.Fd (Algebraic methods)