Brooks, Paul M. (2006) Infrared behaviour and renormalization scheme invariance of QCD observables,

form for the generating functional of one-particle irreducible vertices of the O(N) (non)–linear σ–models in the leading 1/N approximation.We show that this incorporates all infrared behaviour correctly both in linear and non-linear σ – models. These techniques provide an alternative to chiral

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The possible infrared behaviour of the gluon propagator is studied analytically, using the Schwinger-Dyson equations, in both the axial and the Landau gauge. The possibility of a gluon propagator less singular than 1/k 2 when k 2 → 0 is investigated and found to be inconsistent, despite claims

Applying the recently obtained results on the renormalization of soft supersymmetry-breaking parameters, we investigate the infrared behaviour of the softly broken supersymmetric QCD as well as its dual theory in the conformal window. Under general assumptions on β-functions, it is shown

We study the infrared behaviour of the pure Yang-Mills correlators using relations that are well defined in the non-perturbative domain. These are the Slavnov-Taylor identity for three-gluon vertex and the Schwinger-Dyson equation for ghost propagator in the Landau gauge. We also use several inputs

An action principle technique is used to examine the infra-red problem in the effective action for gauge field theories. It is shown by means of a dynamical analogy that the renormalization group and the ansatz of non-local sources can be simultaneously understood through generalized variations

. The resulting running coupling possesses an infrared fixed point, αS(0) = 8.92/Nc for all gauge groups SU(Nc). Above one GeV the running coupling rapidly approaches its perturbative form.

Abstract. In the framework of causal perturbation theory we consider a massive scalar field coupled to gravity. In the field theoretic approach to quantum gravity (QG) we start with a massless second rank tensor field. This tensor field is then quantized in a covariant way in Minkowski space. This article deals with the adiabatic limit for graviton radiative corrections in a scattering process of two massive scalar particles. We compute the differential cross-section for bremsstrahlung processes in which one of the outgoing particles emits a graviton of low energy, a so called soft graviton. Since the emited graviton will not be detected we have to integrate over all soft gravitons. 1.

Recent studies of QCD Green’s functions and their applications in hadronic physics are reviewed. We discuss the definition of the generating functional in gauge theories, in particular, the rôle of redundant degrees of freedom, possibilities of a complete gauge fixing versus gauge fixing in presence of Gribov copies, BRS invariance and positivity. The apparent contradiction between positivity and colour antiscreening in combination with BRS invariance in QCD is considered. Evidence for the violation of positivity by quarks and transverse gluons in the covariant gauge is collected, and it is argued that this is one manifestation of confinement. We summarise the derivation of the Dyson–Schwinger equations (DSEs) of QED and QCD. For the latter, the implications of BRS invariance on the Green’s functions are explored. The possible influence of instantons on DSEs is discussed in a two-dimensional model. In QED in 2+1 and 3+1 dimensions, the solutions for Green’s functions provide tests of truncation schemes which can under certain circumstances be extended to the DSEs of QCD. We discuss some limitations of such extensions and assess the validity of assumptions for QCD as motivated from studies