Yang-Mills fields and the lattice

TL;DR

This paper discusses the use of lattice techniques to study Yang-Mills fields in the strong coupling regime, crucial for understanding strong nuclear forces and quark confinement from first principles.

Contribution

It reviews the historical development and success of lattice methods in non-perturbative analysis of Yang-Mills theories and strong interactions.

Findings

Lattice techniques effectively demonstrate quark confinement.

Non-perturbative properties of strong interactions are obtained from first principles.

Lattice serves as an ultraviolet regulator avoiding perturbative expansion.

Abstract

The Yang-Mills theory lies at the heart of our understanding of elementary particle interactions. For the strong nuclear forces, we must understand this theory in the strong coupling regime. The primary technique for this is the lattice. While basically an ultraviolet regulator, the lattice avoids the use of a perturbative expansion. I discuss some of the historical circumstances that drove us to this approach, which has had immense success, convincingly demonstrating quark confinement and obtaining crucial properties of the strong interactions from first principles.