Llanes Estrada, Felipe JoséAlkofer, R.Fischer, C. S.Schwenzer, K.2023-06-202023-06-202007-100218-301310.1142/S0218301307008367https://hdl.handle.net/20.500.14352/50796© World Scientific Publishing Company R. Alkofer Alkofer thanks the organizers of X Hadron Physics 2007 for inviting him to give a seminar at this extraordinarily interesting workshop. This work has been supported in part by the DFG under contract AL 279/5-1 and by the FWF under contract M979-N16. Hadron Physics Workshop (10. 2007. Florianopolis, Brasil)The infrared behavior of Landau gauge QCD vertex functions is investigated employing a skeleton expansion of the Dyson Schwinger and Renormalization Group equations. Results for the ghost-gluon, three-gluon, four-gluon and quark-gluon vertex functions are presented. Positivity violation of the gluon propagator, and thus gluon confinement, is demonstrated. Results of the Dyson-Schwinger equations for a finite volume are compared to corresponding lattice data. It is analytically demonstrated that a linear rising potential between heavy quarks can be generated by infrared singularities in the dressed quark-gluon vertex. The selfconsistent mechanism that generates these singularities necessarily entails the scalar Dirac amplitudes of the full vertex and the quark propagator. These can only be present when chiral symmetry is broken, either explicitly or dynamically.engjournal articlehttp://dx.doi.org/10.1142/S0218301307008367http://arxiv.org/abs/0707.1286http://www.worldscientific.comopen access53Dyson-Schwinger EquationsYang-Mills TheoryRenormalizationPropagatorsPhysicsGluonFieldFísica (Física)22 Física