English

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