A Note on Coupled Dirac Operators

TL;DR

This paper explores specific solutions to the Dirac equation coupled with vector bundles and connections, relevant in the context of Yang-Mills equations and vector bundles on Riemann surfaces.

Contribution

It provides concrete solutions to coupled Dirac operators, advancing understanding in geometric analysis and mathematical physics.

Findings

Explicit solutions to coupled Dirac equations presented

Connections to Yang-Mills theory elucidated

Applications to vector bundles on Riemann surfaces discussed

Abstract

The article considers some concrete solutions to the Dirac equation coupled to a vector bundle with connection, arising in the study of Yang-Mills equations and vector bundles on Riemann surfaces.