A diagrammatic categorification of the fermion algebra
Mathematical Physics
2013-10-04 v1 math.MP
Quantum Algebra
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.
Keywords
Cite
@article{arxiv.1307.4522,
title = {A diagrammatic categorification of the fermion algebra},
author = {Bing-Sheng Lin and Zhi-Xi Wang and Ke Wu and Zi-Feng Yang},
journal= {arXiv preprint arXiv:1307.4522},
year = {2013}
}
Comments
10 pages, many TikZ figures. To appear in Chin. Phys. B