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A diagrammatic categorification of the fermion algebra

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.

preprint2013arXivOpen access
Bing-Sheng LinZhi-Xi WangKe WuZi-Feng Yang
math-phmath.QAmath.MP
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Open access4 authors3 topics
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Bing-Sheng LinZhi-Xi WangKe WuZi-Feng Yang

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