Non-perturbative QCD and QED vertices from first principles: combining continuum methods with lattice results

Abstract

The aim of this project is to study the quark-gluon vertex in QCD combining continuum techniques, that take into account the constraints due to the Slavnov-Taylor identities to solve the Dyson-Schwinger equations, and the available lattice QCD results for the quark-gluon vertex, the propagators and three gluon vertex. Issues as the momentum dependence of the various vertex form factors and the inclusion of the vertex transverse operators will be addressed by extending our previous works. Further, we aim to understand which vertex operators contribute to chiral symmetry breaking, i.e. to the problem of the quark mass generation. Simultaneously, we aim to study the photon-fermion vertex in QED using a set of Dyson-Schwinger equations for various Green functions combined with the corresponding Ward-Takahashi identities. For the QED vertex the goals are to perform a non-perturbative investigation of the vertex, to arrive at a complete description of the vertex, and to study its gauge dependence within the linear covariant gauges. We also plan to start investigating the solution of the Dyson-Schwinger equations in Minkowski space for QED and QCD with the help of integral representations as the Källén-Lehmann and its generalizations. (AU)