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arXiv · 1307.4522

A diagrammatic categorification of the fermion algebra

Bing-Sheng Lin·Zhi-Xi Wang·Ke Wu·Zi-Feng Yang
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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 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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Bing-Sheng Lin, Zhi-Xi Wang, Ke Wu, Zi-Feng Yang. 2013-07-17. A diagrammatic categorification of the fermion algebra. https://doi.org/10.1088/1674-1056/22/10/100201

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