Dirac-Connes Operator on Discrete Abelian Groups and Lattices

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.

Latex, 9 pages, no figures; References added

References in corpus (8)

• Gravity coupled with matter and foundation of non-commutative geometry
• The Fermion Doubling Problem and Noncommutative Geometry
• Discrete differential calculus, graphs, topologies and gauge theory
• Noncommutative Geometry of Finite Groups
• Differential calculus and gauge theory on finite sets
• Noncommutative Geometry and Gauge Theories on Discrete Groups
• Some aspects of noncommutative geometry and physics
• The Dirac Operator over Abelian Finite Groups

Cited by in corpus (2)

• Wilson Action of Lattice Gauge Fields with An Additional Term from Noncommutative Geometry
• A New Solution to Ginsparg-Wilson Relation from Generalized Staggered Fermion