Local well-posedness of the coupled Yang-Mills and Dirac system for low regularity data

TL;DR

This paper proves local well-posedness for the coupled Yang-Mills and Dirac system in 3+1 dimensions with minimal regularity data, extending previous results for smooth data and leveraging null condition properties.

Contribution

It establishes local well-posedness for low regularity initial data in the coupled Yang-Mills-Dirac system, generalizing prior smooth data results.

Findings

Proves local well-posedness with minimal regularity assumptions.

Utilizes null condition to handle nonlinear terms.

Extends previous Yang-Mills results to coupled system.

Abstract

We consider the classical Yang-Mills system coupled with a Dirac equation in 3+1 dimensions. Using that most of the nonlinear terms fulfill a null condition we prove local well-posedness for data with minimal regularity assumptions. This problem for smooth data was solved forty years ago by Y. Choquet-Bruhat and D. Christodoulou. Our result generalizes a similar result for the Yang-Mills equation by S. Selberg and A. Tesfahun.