Differential Dyson–Schwinger equations for quantum chromodynamics

Abstract

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.

Diluted mass gap in strongly coupled non-local Yang-Mills

“…where we used the result given in [26] for the non-local Dirac equation and omitted internal degrees of freedom. Anyway, this kind of model can imply breaking of chiral symmetry and confinement as recently shown [64]. This kind of model can also describe bounded states and all the properties of QCD at very low-energy can be translated to the non-local case.…”

“…The technique is the following [64]. Let us introduce a set of symbols: η−symbols for SU(N) (this can be possibly extend to the SO(N) case in a straightforward way.…”

“…For the sake of simplicity, we work out the case for SU (2) where the proof of their existence is straightforward. Indeed, in this case, they can be defined as [64,65] η a µ = ((0, 1, 0, 0), (0, 0, 1, 0), (0, 0, 0, 1)),…”

On a novel evalutation of the hadronic contribution to the muon's $g-2$ from QCD

“…In order to study these equations, we use the method proposed by Bender, Milton and Savage [13], details of which can found in Refs. [12,[14][15][16][17]. For the purpose of this publication we sketch the main steps here, skipping contributions from BRST ghosts for simplicity.…”

“…A first attempt in this direction was given in Ref. [12] in order to determine the proper low-energy limit of the theory 1 . In this work, we fix an error in this publication and show how the effective NJL model comes out naturally from QCD.…”