A Categorification of the Boson Oscillator  

作　　者：LIN Bing-Sheng WU Ke 林冰生;吴可(School of Mathematical Sciences,Capital Normal University,Beijing 100048,China)

机构地区：[1]School of Mathematical Sciences,Capital Normal University,Beijing 100048,China

出　　处：《Communications in Theoretical Physics》2012年第1期34-40,共7页理论物理通讯（英文版）

基　　金：Supported by National Natural Science Foundation of China under Grant Nos. 10975102,10871135,11031005,11075014

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.

关 键 词：CATEGORIFICATION Boson oscillator Fock state Heisenberg algebra 

分 类 号：O413[理学—理论物理]