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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 |
a Department of Mathematics, South China University of Technology, Guangzhou 510641, China;
b School of Mathematical Sciences, Capital Normal University, Beijing 100048, China |
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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.
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Received: 21 March 2013
Revised: 13 April 2013
Accepted manuscript online:
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PACS:
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02.10.Hh
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(Rings and algebras)
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03.65.Ca
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(Formalism)
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03.65.Fd
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(Algebraic methods)
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| Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 10975102, 10871135, 11031005, and 11075014). |
Corresponding Authors:
Lin Bing-Sheng
E-mail: sclbs@scut.edu.cn
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Cite this article:
Lin Bing-Sheng (林冰生), Wang Zhi-Xi (王志玺), Wu Ke (吴可), Yang Zi-Feng (杨紫峰) A diagrammatic categorification of the fermion algebra 2013 Chin. Phys. B 22 100201
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