Infra-Red Behavior of the Running Coupling Constant in QCD

Abstract

In these lectures I will describe a non-perturbative method of studying the infrared (IR) structure of Quantum Chromodynamics (QCD) [1] and then follow with the description of an investigation of the momentum dependence of vertex functions in gauge theories[2], It is widely accepted that these IR singularities may cause color to be confined and hence produce quark confinement. In particular it is argued [3] that an “effective potential” in momentum space between quarks is proportional to g²(q²)/q² where g²(q²) is the running coupling constant which is singular in the IR i.e. as q² → 0. For example if g²(q²)~ l/q² as q² → 0 we can crudely translate this into a potential growing linearly with distance for large distances.