Dirac-Connes Operator on Discrete Abelian Groups and Lattices

2001/01/17 by Jian Dai, Jian S. Dai, Dai, Jian +2
Chemistry · Mathematics · Physics and Astronomy · #Abelian group #Advanced Operator Algebra Research #Algebra over a field #Chemistry #Dirac operator #Elementary abelian group #FOS: Physical sciences #High Energy Physics - Lattice (hep-lat) #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Mathematical physics #Mathematics #Operator (biology) #Pure mathematics #Rank of an abelian group #Spectral Theory in Mathematical Physics #advanced mathematical theories #hep-lat #hep-th #math-ph #math.MP

paper · pdf · doi:10.48550/arxiv.hep-th/0101111

Latex, 9 pages, no figures; References added

openalex publication_date 2001/01/17 · arxiv created 2001/01/22 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

A kind of Dirac-Connes operator defined in the framework of Connes' NCG is introduced on discrete abelian groups; it satisfies a Junk-free condition, and bridges the NCG composed by Dimakis, Müller-Hoissen and Sitarz and the NCG of Connes. Then we apply this operator to d-dimensional lattices.

Citations

• Some aspects of noncommutative geometry and physics
• Connes' Distance Function on One-Dimensional Lattices

Related

• The Dirac Operator over Abelian Finite Groups
• Properties of a New Class of Lattice Dirac Operators
• Dirac Operators and the Calculation of the Connes Metric on arbitrary (Infinite) Graphs
• Remarks on discrete Dirac operators and their continuum limits
• Discrete spectral triples converging to dirac operators