Gauge-invariant field strengths in $QCD$

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.

Comments: Presented to the conference New Trends in Theoretical Physics (Tashkent, 2023)