Geometric Origin of Staggered Fermion: Direct Product K-Cycle

TL;DR

This paper demonstrates how the staggered fermion formalism in lattice gauge theory can be represented using direct product K-cycles in noncommutative geometry, establishing a mathematical correspondence with abelian groups.

Contribution

It introduces a novel geometric framework for staggered fermions using K-cycles, linking lattice structures to noncommutative geometry.

Findings

Staggered fermions can be formulated as direct product K-cycles.

A correspondence between staggered K-cycles and abelian group K-cycles is established.

The approach provides a new geometric perspective on lattice fermions.

Abstract

Staggered formalism of lattice fermion can be cast into a form of direct product K-cycle in noncommutative geometry. The correspondence between this staggered K-cycle and a canonically defined K-cycle for finitely generated abelian group where lattice appears as a special case is proved.