Quasi-Dirac Operators and Quasi-Fermions

TL;DR

This paper explores quasi-spectral triples on a 2D sphere, introducing modified quasi-Dirac operators that differ topologically from standard Dirac operators, expanding the understanding of noncommutative geometry.

Contribution

It constructs equivariant quasi-Dirac operators on the sphere by altering the order-one condition, revealing a new topological sector distinct from the classical case.

Findings

Quasi-Dirac operators are constructed on the sphere.

These operators form a topologically distinct sector.

Modification of the order-one condition is key to the new operators.

Abstract

We investigate examples of quasi-spectral triples over two-dimensional commutative sphere, which are obtained by modifying the order-one condition. We find equivariant quasi-Dirac operators and prove that they are in a topologically distinct sector than the standard Dirac operator.