The electromagnetic form factors GE(q 2 ), GM (q 2 ), and GQ(q 2 ), charge radii, magnetic and quadrupole moments, and decay widths of the light vector mesons ρ + , K * + and K * 0 are calculated in a Lorentz-covariant, Dyson-Schwinger equation based model using algebraic quark propagators that incorporate confinement, asymptotic freedom, and dynamical chiral symmetry breaking, and vector meson Bethe-Salpeter amplitudes closely related to the pseudoscalar amplitudes obtained from phenomenological studies of π and K mesons. Calculated static properties of vector mesons include the charge radii and magnetic moments: r 2 ρ+ 1/2 = 0.61 fm, r 2 K * + 1/2 = 0.54 fm, and r 2 K * 0 = -0.048 fm 2 ; µρ+ = 2.69, µ K * + = 2.37, and µ K * 0 = -0.40. The calculated static limits of the ρ-meson form factors are similar to those obtained from light-front quantum mechanical calculations, but begin to differ above q 2 = 1 GeV 2 due to the dynamical evolution of the quark propagators in our approach.

We study a model Dyson-Schwinger equation for the quark propagator closed using an Ansatz for the gluon propagator of the form D(q) -q2/[(q2)' + b4] and two Ansatze for the quark-gluon vertex: the minimal Ball-Chiu form and the modified form suggested by Curtis and Pennington. Using the quark condensate as an order parameter, we find that there is a critical value of b = b, such that the model does not support dynamical chiral symmetry breaking for b > b,. We discuss and apply a confinement test which suggests that, for all values of b, the quark propagator in the model is not confining. Together these results suggest that this Ansatz for the gluon propagator is inadequate as a model since it does not yield the expected behavior of QCD.

We elucidate constraints imposed by confinement and dynamical chiral symmetry breaking on the infrared behaviour of the dressed-quark and -gluon propagators, and dressed-quark-gluon vertex. In covariant gauges the dressing of the gluon propagator is completely specified by P(k 2 ) := 1/[1+ Π(k 2 )], where Π(k 2 ) is the vacuum polarisation. In the absence of particle-like singularities in the dressed-quark-gluon vertex, extant proposals for the dressed-gluon propagator that manifest P(k 2 = 0) = 0 and max(P(k 2 )) ∼ 10 neither confine quarks nor break chiral symmetry dynamically. This class includes all existing estimates of P(k 2 ) via numerical simulations.Key words: Gluon and quark Schwinger functions; Dynamical Chiral Symmetry Breaking; Confinement; Dyson-Schwinger equations; Lattice-QCD PACS: 11.30. Rd, 12.38.Aw, 12.38.Lg, 24.85.+p Strong interaction phenomena are characterised by dynamical chiral symmetry breaking (DCSB) and colour confinement. At low energy, DCSB is the more important; for example, in its absence the π-and ρ-mesons would be nearly degenerate and at the simplest observational level that would lead to a markedly different line of nuclear stability. These phenomena can be related to the infrared behaviour of elementary Schwinger functions in QCD and herein we elucidate some constraints they place on this behaviour.As described pedagogically in Ref.[1], DCSB can be studied using the QCD "gap equation"; i.e., the Dyson-Schwinger equation (DSE) for the renormalised dressed-quark propagator (connected, 2-point, dressed-quark Schwinger function), S(p):

We present results from a study of subtractive renormalization of the fermion propagator Dyson-Schwinger equation (DSE) in massive strongcoupling quenched QED 4 . Results are compared for three different fermionphoton proper vertex Ansätze: bare γ µ , minimal Ball-Chiu, and CurtisPennington. The procedure is straightforward to implement and numerically stable. This is the first study in which this technique is used and it should prove useful in future DSE studies, whenever renormalization is required in numerical work.

We study renormalized quenched strong-coupling QED in four dimensions in arbitrary covariant gauge, in the Dyson-Schwinger equation formalism. Above the chiral critical coupling, we show that there is no finite chiral limit. This behaviour is found to be independent of the detailed choice of proper vertex, provided that the vertex is consistent with the Ward-Takahashi identity and multiplicative renormalizability. The finite solutions previously reported lie in an unphysical regime of the theory with multiple solutions and oscillating mass functions. This study is consistent with the assertion that strong coupling QED 4 does not have a continuum limit in the conventional sense.