Infrared Gluon and Ghost Propagators

TL;DR

This paper derives the form of the infrared gluon propagator in quantum Yang-Mills theory by establishing a classical mapping with scalar field theories, and confirms the results with lattice computations, showing a finite propagator at zero momentum.

Contribution

It demonstrates a classical mapping between Yang-Mills and scalar theories in the infrared, providing an analytical form of the gluon propagator consistent with lattice results.

Findings

Infrared gluon propagator is finite at zero momentum.

Ghost propagator diverges as 1/p^{2+2κ} with κ=0.

Results agree with recent lattice computations.

Abstract

We derive the form of the infrared gluon propagator by proving a mapping in the infrared of the quantum Yang-Mills and $\lambda\phi^4$ theories. The equivalence is complete at a classical level. But while at a quantum level, the correspondence is spoiled by quantum fluctuations in the ultraviolet limit, we prove that it holds in the infrared where the coupling constant happens to be very large. The infrared propagator is then obtained from the quantum field theory of the scalar field producing a full spectrum. The results are in fully agreement with recent lattice computations. We get a finite propagator at zero momentum, the ghost propagator going to infinity as $1/p^{2+2\kappa}$ with $\kappa=0$.