We survey contemporary studies of hadrons and strongly interacting quarks using QCD's DysonSchwinger equations, addressing: aspects of confinement and dynamical chiral symmetry breaking; the hadron spectrum; hadron elastic and transition form factors, from small-to large-Q 2 ; parton distribution functions; the physics of hadrons containing one or more heavy quarks; and properties of the quark gluon plasma.

We present a unified study of nucleon and ∆ elastic and transition form factors, and compare predictions made using a framework built upon a Faddeev equation kernel and interaction vertices that possess QCD-like momentum dependence with results obtained using a symmetry-preserving treatment of a vector ⊗ vector contact-interaction. The comparison emphasises that experiments are sensitive to the momentum dependence of the running couplings and masses in the strong interaction sector of the Standard Model and highlights that the key to describing hadron properties is a veracious expression of dynamical chiral symmetry breaking in the bound-state problem. Amongst the results we describe, the following are of particular interest:possesses a zero at Q 2 = 9.5 GeV 2 ; any change in the interaction which shifts a zero in the proton ratio to larger Q 2 relocates a zero inthere is likely a value of momentum transfer above which G n E > G p E ; and the presence of strong diquark correlations within the nucleon is sufficient to understand empirical extractions of the flavour-separated form factors. Regarding the ∆(1232)-baryon, we find that, inter alia: the electric monopole form factor exhibits a zero; the electric quadrupole form factor is negative, large in magnitude, and sensitive to the nature and strength of correlations in the ∆(1232) Faddeev amplitude; and the magnetic octupole form factor is negative so long as rest-frame P -and D-wave correlations are included. In connection with the N → ∆ transition, the momentum-dependence of the magnetic transition form factor, G * M , matches that of G n M once the momentum transfer is high enough to pierce the meson-cloud; and the electric quadrupole ratio is a keen measure of diquark and orbital angular momentum correlations, the zero in which is obscured by meson-cloud effects on the domain currently accessible to experiment. Importantly, within each framework, identical propagators and vertices are sufficient to describe all properties discussed herein. Our analysis and predictions should therefore serve as motivation for measurement of elastic and transition form factors involving the nucleon and its resonances at high photon virtualities using modern electron-beam facilities.

A dressed-quark core contribution to nucleon electromagnetic form factors is calculated. It is defined by the solution of a Poincaré covariant Faddeev equation in which dressed-quarks provide the elementary degree of freedom and correlations between them are expressed via diquarks. The nucleonphoton vertex involves a single parameter; i.e., a diquark charge radius. It is argued to be commensurate with the pion's charge radius. A comprehensive analysis and explanation of the form factors is built upon this foundation. A particular feature of the study is a separation of form factor contributions into those from different diagram types and correlation sectors, and subsequently a flavour separation for each of these. Amongst the extensive body of results that one could highlight are: r n,u 1 > r n,d 1 , owing to the presence of axial-vector quark-quark correlations; and for both the neutron and proton the ratio of Sachs electric and magnetic form factors possesses a zero.