Infrared Gluon and Ghost Propagators

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 $\kappa=0$.Comment: 7 pages, no figure. After proofs correction. To appear in Physics Letters

Differential Dyson-Schwinger equations for quantum chromodynamics

Using a technique devised by Bender, Milton and Savage, we derive the Dyson-Schwinger equations for quantum chromodynamics in differential form. We stop our analysis to the two-point functions. The 't~Hooft limit of color number going to infinity is derived showing how these equations can be cast into a treatable even if approximate form. It is seen how this limit gives a sound description of the low-energy behavior of quantum chromodynamics by discussing the dynamical breaking of chiral symmetry and confinement, providing a condition for the latter. This approach exploits a background field technique in quantum field theory.Comment: 20 pages, 2 figures. Version accepted for publication in European Physical Journal