Gauge-invariant field strengths in $QCD$

TL;DR

This paper explores gauge-invariant field strengths in QCD, highlighting their role in confinement, their constrained correlation functions, and their significance in understanding the vacuum through lattice data.

Contribution

It introduces the concept of gauge-invariant field strengths defined via parallel transports and analyzes their properties and constraints in QCD.

Findings

Gauge-invariant field strengths are crucial in understanding confinement.

Differentiability and symmetry impose strong constraints on their correlation functions.

They facilitate the analysis of the QCD vacuum using lattice data.

Abstract

Gauge-invariant field strengths, defined as parallel transports to infinity of ordinary field strengths, naturally emerge in a few physical phenomena governed by $QCD$. One of them is confinement of colour. Despite the arbitrariness in their definition coming from the freedom in the choice of the path of the parallel transport to infinity, the request of differentiability with respect to the position $x$ strongly constrains their correlation functions. Strong constraints also come from translation and Lorentz invariance. Gauge invariant field strengths also appear in the non abelian Stokes theorem, and allow to understand basic properties of the vacuum by use of lattice data.