Noncommutative Geometry of Lattice and Staggered Fermions
High Energy Physics - Theory
2009-11-07 v2 High Energy Physics - Lattice
Mathematical Physics
math.MP
Abstract
Differential structure of a d-dimensional lattice, which is essentially a noncommutative exterior algebra, is defined using reductions in first order and second order of universal differential calculus in the context of noncommutative geometry (NCG) developed by Dimakis et al. This differential structure can be realized adopting a Dirac-Connes operator proposed by us recently within Connes' NCG. With matrix representations being specified, our Dirac-Connes operator corresponds to staggered Dirac operator, in the case that dimension of the lattice equals to 1, 2 and 4.
Cite
@article{arxiv.hep-th/0101130,
title = {Noncommutative Geometry of Lattice and Staggered Fermions},
author = {Jian Dai and Xing-Chang Song},
journal= {arXiv preprint arXiv:hep-th/0101130},
year = {2009}
}
Comments
Latex; 13 pages; no figures. References added. Accepted by Phys. Lett. B