Strongly-coupled unquenched QED(4) propagators using Schwinger-Dyson equations

We study unquenched QED in four dimensions using renormalized Schwinger-Dyson equations and focus on the behaviour of the fermion and photon propagators. For this purpose we use an improved Kızılersü-Pennington (KP) vertex which respects gauge invariance, multiplicative renormalizability for the massless case, agrees with perturbation theory in the weak coupling regime, and is free of kinematic singularities. We find that the KP vertex performs very well as expected especially in comparison with other vertex choices. We find that the Landau pole problem familiar from perturbative QED persists in the nonperturbative case with the renormalized inverse photon propagator having zero crossing.Ayşe Kızılersü, Tom Sizer, and Anthony G. William

Multiplicative renormalizability and quark propagator

The renormalized Dyson-Schwinger equation for the quark propagator is studied, in Landau gauge, in a novel truncation which preserves multiplicative renormalizability. The renormalization constants are formally eliminated from the integral equations, and the running coupling explicitly enters the kernels of the new equations. To construct a truncation which preserves multiplicative renormalizability, and reproduces the correct leading order perturbative behavior, non-trivial cancellations involving the full quark-gluon vertex are assumed in the quark self-energy loop. A model for the running coupling is introduced, with infrared fixed point in agreement with previous Dyson-Schwinger studies of the gauge sector, and with correct logarithmic tail. Dynamical chiral symmetry breaking is investigated, and the generated quark mass is of the order of the extension of the infrared plateau of the coupling, and about three times larger than in the Abelian approximation, which violates multiplicative renormalizability. The generated scale is of the right size for hadronic phenomenology, without requiring an infrared enhancement of the running coupling.Comment: 17 pages; minor corrections, comparison to lattice results added; accepted for publication in Phys. Rev.

Running coupling and fermion mass in strong coupling QED

Simple toy model is used in order to exhibit the technique of extracting the non-perturbative information about Green's functions in Minkowski space. The effective charge and the dynamical electron mass are calculated in strong coupling 3+1 QED by solving the coupled Dyson-Schwinger equations for electron and photon propagators. The minimal Ball-Chiu vertex was used for simplicity and we impose the Landau gauge fixing on QED action. The solution obtained separately in Euclidean and Minkowski space were compared, the latter one was extracted with the help of spectral technique.Comment: 23 pages, 4 figures, v4: revised and extended version, one introductory section adde

On Nonperturbative Calculations in Quantum Electrodynamics

A new approach to nonperturbative calculations in quantum electrodynamics is proposed. The approach is based on a regular iteration scheme for solution of Schwinger-Dyson equations for generating functional of Green functions. The approach allows one to take into account the gauge invariance conditions (Ward identities) and to perform the renormalization program. The iteration scheme can be realized in two versions. The first one ("perturbative vacuum") corresponds to chain summation in the diagram language. In this version in four-dimensional theory the non-physical singularity (Landau pole) arises which leads to the triviality of the renormalized theory. The second version ("nonperturbative vacuum") corresponds to ladder summation and permits one to make non-perturbative calculations of physical quantities in spite of the triviality problem. For chiral-symmetrical leading approximation two terms of the expansion of the first-step vertex function over photon momentum are calculated. A formula for anomalous magnetic moment is obtained. A problem of dynamical chiral symmetry breaking (DCSB) is considered, the calculations are performed for renormalized theory in Minkowsky space. In the strong coupling region DCSB-solutions arise. For the renormalized theory a DCSB-solution is also possible in the weak coupling region but with a subsidiary condition on the value of $\alpha$.Comment: 31 pages, Plain LaTex, no figures. Journal version: some discussion and refs. are adde