A diagrammatic categorification of the fermion algebra  

作　　者：林冰生 王志玺 吴可 杨紫峰 

机构地区：[1]Department of Mathematics,South China University of Technology [2]School of Mathematical Sciences,Capital Normal University

出　　处：《Chinese Physics B》2013年第10期61-66,共6页中国物理B（英文版）

基　　金：Project supported by the National Natural Science Foundation of China(Grant Nos.10975102,10871135,11031005,and 11075014)

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.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.

关 键 词：CATEGORIFICATION fermion algebra 

分 类 号：O153[理学—数学]