Strong QCD and Dyson–Schwinger equations

Abstract

The real-world properties of quantum chromodynamics (QCD) – the strongly interacting piece of the Standard Model – are dominated by two emergent phenomena: confinement; namely, the theory’s elementary degrees-of-freedom – quarks and gluons – have never been detected in isolation; and dynamical chiral symmetry breaking (DCSB), which is a remarkably effective mass generating mechanism, responsible for the mass of more than 98% of visible matter in the Universe. These phenomena are not apparent in the formulae that define QCD, yet they play a principal role in determining Nature’s observable characteristics. Much remains to be learnt before confinement can properly be understood. On the other hand, the last decade has seen important progress in the use of relativistic quantum field theory, so that we can now explain the origin of DCSB and are beginning to demonstrate its far-reaching consequences. Dyson–Schwinger equations have played a critical role in these advances. These lecture notes provide an introduction to Dyson–Schwinger equations (DSEs), QCD and hadron physics, and illustrate the use of DSEs to predict observable phenomena.