Local well-posedness of the coupled Yang-Mills and Dirac system in temporal gauge

TL;DR

This paper proves local well-posedness for the coupled Yang-Mills and Dirac system in 3+1 dimensions under small data and minimal regularity assumptions, extending classical results to a new gauge setting.

Contribution

It establishes local well-posedness for the coupled system in temporal gauge with minimal regularity, building on prior work in smooth data and other gauges.

Findings

Proves local well-posedness for small data in temporal gauge.

Utilizes null condition to handle nonlinear terms.

Extends classical results to lower regularity settings.

Abstract

We consider the classical Yang-Mills system coupled with a Dirac equation in 3+1 dimensions in temporal gauge. Using that most of the nonlinear terms fulfill a null condition we prove local well-posedness for small data with minimal regularity assumptions. This problem for smooth data was solved forty years ago by Y. Choquet-Bruhat and D. Christodoulou. The corresponding problem in Lorenz gauge was considered recently by the author in [P1].