From Euclidean to Minkowski space with the Cauchy-Riemann equations

We present an elementary method to obtain Green's functions in non-perturbative quantum field theory in Minkowski space from calculated Green's functions in Euclidean space. Since in non-perturbative field theory the analytical structure of amplitudes is many times unknown, especially in the presence of confined fields, dispersive representations suffer from systematic uncertainties. Therefore we suggest to use the Cauchy-Riemann equations, that perform the analytical continuation without assuming global information on the function in the entire complex plane, only in the region through which the equations are solved. We use as example the quark propagator in Landau gauge Quantum Chromodynamics, that is known from lattice and Dyson-Schwinger studies in Euclidean space. The drawback of the method is the instability of the Cauchy-Riemann equations to high-frequency noise, that makes difficult to achieve good accuracy. We also point out a few curiosities related to the Wick rotation.Comment: 12 pages in EPJ double-column format, 16 figures. This version: added paragraph, two reference

Renormalizability of a quark-gluon model with soft BRST breaking in the infrared region

We prove the renormalizability of a quark-gluon model with a soft breaking of the BRST symmetry, which accounts for the modification of the large distance behavior of the quark and gluon correlation functions. The proof is valid to all orders of perturbation theory, by making use of softly broken Ward identities.Comment: 20 pages, no figures. Preprint number added in v2

The chiral and angular momentum content of the rho-meson

It is possible to define and calculate in a gauge-invariant manner the chiral as well as the partial wave content of the quark-antiquark Fock component of a meson in the infrared, where mass is generated. Using the variational method and a set of interpolators that span a complete chiral basis we extract in a lattice QCD Monte Carlo simulation with two dynamical light quarks the orbital angular momentum and spin content of the rho-meson. We obtain in the infrared a simple 3S1 component as a leading component of the rho-meson with a small admixture of the 3D1 partial wave, in agreement with the SU(6) flavor-spin symmetry.Comment: 23 pages, 4 figures, 2 table

The Infrared Behaviour of the Pure Yang-Mills Green Functions

We review the infrared properties of the pure Yang-Mills correlators and discuss recent results concerning the two classes of low-momentum solutions for them reported in literature; i.e. decoupling and scaling solutions. We will mainly focuss on the Landau gauge and pay special attention to the results inferred from the analysis of the Dyson-Schwinger equations of the theory and from "{\it quenched}" lattice QCD. The results obtained from properly interplaying both approaches are strongly emphasized.Comment: Final version to be published in FBS (54 pgs., 11 figs., 4 tabs