Infrared Gluon and Ghost Propagators

Abstract

We derive the form of the infrared gluon propagator by proving a mapping in the infrared of the quantum Yang-Mills and $\lambda {\varphi }^4$ 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 $\kappa =0$.

7 pages, no figure. After proofs correction. To appear in Physics Letters B

References in corpus (5)

• Large volume behaviour of Yang-Mills propagators
• Green Function Method for Nonlinear Systems
• Green functions and nonlinear systems: Short time expansion
• Proof of triviality of $\lambda {\varphi }^4$ theory
• Infrared analysis of quantum field theories

Cited by in corpus (1)

• Mapping a Massless Scalar Field Theory on a Yang-Mills Theory: Classical Case