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International Journal of Theoretical Physics

, Volume 56, Issue 7, pp 2071–2080 | Cite as

A Groupoidification of the Fermion Algebra

  • Wei Chen
  • Bingsheng Lin
Article

Abstract

In this paper, we consider the groupoidification of the fermion algebra. We construct a groupoid as the categorical analogues of the fermionic Fock space, and the creation and annihilation operators correspond to spans of groupoids. The categorical fermionic Fock states have some extra structures comparing with the normal forms. We also construct a 2-category of spans of groupoids corresponding to the fermion algebra. The relations of the morphisms in this 2-category are consistent with those in the graphical category which is represented by string diagrams. One may use these formalisms to describe the fermion systems more finely, and study some additional properties of the fermion systems.

Keywords

Groupoidification Fermion algebra Categorification 2-category 

Notes

Acknowledgements

This work is supported by the National Natural Science Foundation of China (Grant Nos. 11405060, 11571119).

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Copyright information

© Springer Science+Business Media New York 2017

Authors and Affiliations

  1. 1.School of MathematicsSouth China University of TechnologyGuangzhouChina

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