Truncated Schwinger-Dyson Equations and Gauge Covariance in QED3

We study the Landau-Khalatnikov-Fradkin transformations (LKFT) in momentum space for the dynamically generated mass function in QED3. Starting from the Landau gauge results in the rainbow approximation, we construct solutions in other covariant gauges. We confirm that the chiral condensate is gauge invariant as the structure of the LKFT predicts. We also check that the gauge dependence of the constituent fermion mass is considerably reduced as compared to the one obtained directly by solving SDE.Comment: 17 pages, 11 figures. v3. Improved and Expanded. To appear in Few Body System

Non-perturbative Aspects of Schwinger-Dyson Equations

Schwinger-Dyson equations (SDEs) provide a natural staring point to study non-perturbative phenomena such as dynamical chiral symmetry breaking in gauge field theories. We briefly review this research in the context of quenched quantum electrodynamics (QED) and discuss the advances made in the gradual improvement of the assumptions employed to solve these equations. We argue that these attempts render the corresponding studies more and more reliable and suitable for their future use in the more realistic cases of unquenched QED, quantum chromodynamics (QCD) and models alternative to the standard model of particle physics.Comment: 8 pages, 1 figure, Talk given at the X Mexican School of Particles and Fields, Playa del Carmen, Mexico, 2002 (uses AIP style files

Fermion Propagator in Quenched QED3 in the light of the Landau-Khalatnikov-Fradkin transformation

We study the gauge dependence of the fermion propagator in quenched QED3 with and without dynamical symmetry breaking in the light of its Landau-Khalatnikov-Fradkin Transformation (LKFT). In the former case, starting with the massive bare propagator in the Landau gauge, we obtain non perturbative propagator in an arbitrary covariant gauge. At the one-loop level it yields exact wavefunction renormalization and correct $(\alpha \xi)$ terms for the mass fuction. Also, we obtain valuable information for the higher order perturbative expansion of the propagator. As for the case of dynamical chiral symmetry breaking, we start by approximating the numerical solution to the Schwinger-Dyson equation in Landau gauge in the rainbow approximation in terms of analytic functions. We then LKF transform this result to obtain the dynamically generated fermion propagator in an arbitrary covariant gauge. We find that the results obtained have nice qualitative features. We also extend this exercise to the cases involving more reliable ans\"atze for the vertex and encounter similar (and improved) qualitative features.Comment: 6 pages, 6 figures. Contribution to the Proceedings of QCD Downunder 2004 Workshop, held at the Special Centre for the Subatomic Structure of Matter, University of Adelaide, March, 2004. Uses espcrc2.st

Non-perturbative Fermion Propagator for the Massless Quenched QED3

For massless quenched QED in three dimensions, we evaluate a non-perturbative expression for the fermion propagator which agrees with its two loop perturbative expansion in the weak coupling regime. This calculation is carried out by making use of the Landau-Khalatnikov-Fradkin transformations. Any improved construction of the fermion-boson vertex must make sure that the solution of the Schwinger-Dyson equation for the fermion propagator reproduces this result. For two different gauges, we plot the fermion propagator against momentum. We then make a comparison with a similar plot, using the earlier expression for the fermion propagator, which takes into account only the one loop result.Comment: 11 pages, 3 figures, to appear in Phys. Lett.

Dynamical quarks effects on the gluon propagation and chiral symmetry restoration

We exploit the recent lattice results for the infrared gluon propagator with light dynamical quarks and solve the gap equation for the quark propagator. Chiral symmetry breaking and confinement (intimately tied with the analytic properties of QCD Schwinger functions) order parameters are then studied.Comment: Contribution to QCD-TNT-III: "From quarks and gluons to hadronic matter: A bridge too far?

Constructing the fermion-boson vertex in QED3

We derive perturbative constraints on the transverse part of the fermion-boson vertex in massive QED3 through its one loop evaluation in an arbitrary covariant gauge. Written in a particular form, these constraints naturally lead us to the first non-perturbative construction of the vertex, which is in complete agreement with its one loop expansion in all momentum regimes. Without affecting its one-loop perturbative properties, we also construct an effective vertex in such a way that the unknown functions defining it have no dependence on the angle between the incoming and outgoing fermion momenta. Such a vertex should be useful for the numerical study of dynamical chiral symmetry breaking, leading to more reliable results.Comment: 13 pages, 2 figure

Fermions in odd space-time dimensions: back to basics

It is a well known feature of odd space-time dimensions $d$ that there exist two inequivalent fundamental representations $A$ and $B$ of the Dirac gamma matrices. Moreover, the parity transformation swaps the fermion fields living in $A$ and $B$. As a consequence, a parity invariant Lagrangian can only be constructed by incorporating both the representations. Based upon these ideas and contrary to long held belief, we show that in addition to a discrete exchange symmetry for the massless case, we can also define chiral symmetry provided the Lagrangian contains fields corresponding to both the inequivalent representations. We also study the transformation properties of the corresponding chiral currents under parity and charge conjugation operations. We work explicitly in 2+1 dimensions and later show how some of these ideas generalize to an arbitrary number of odd dimensions.Comment: 8 pages, no figure