K\"allen-Lehman Representation and the Gluon Propagator

TL;DR

This paper uses the Kallen-Lehman representation to prove that the gluon propagator remains finite in the infrared and derives its functional form, enabling comparison of lattice results with experimental data for glueball spectra.

Contribution

It introduces a novel analytical proof that the gluon propagator does not vanish in the infrared and provides a specific functional form for it.

Findings

Gluon propagator cannot go to zero in the infrared

Derived the explicit functional form of the gluon propagator

Facilitates comparison of lattice results with experimental glueball spectra

Abstract

We exploit the Kallen-Lehman representation of the two-point Green function to prove that the gluon propagator cannot go to zero in the infrared limit. We are able to derive also the functional form of it. This means that current results on the lattice can be used to derive the scalar glueball spectrum to be compared both with experiments and different aimed lattice computations.