After having explored various basic aspects of quantum field theory in Chapter 1 and functional methods in Chapter 2, we now turn to non-Abelian gauge theories (mostly with an SU(N) gauge group). The problems in this chapter explore various mathematical questions relevant for non-Abelian gauge theories (in particular, manipulations of su(N) generators), some questions related to their perturbative expansion, as well as some non-perturbative ones, in particular in connection with the rich structure of ground states in Yang–Mills theory.

The theory of quantum chromodynamics (QCD) is introduced. Features of QCD as the nontrivial vacuum due to quark and gluon condensate and asymptotic freedom at high-energy scales are discussed. The concept of perturbative QCD and the running of the coupling constant is established. The equation of state of QCD at high temperatures from lattice QCD is reviewed and confronted with perturbative QCD calculations. The QCD equation of state at high baryon density is discussed. Properties of selfbound stars are developed where the equation of state has a nonvanishing pressure at a nonvanishing energy density. The mass–radius relation of pure quark stars is examined and compared to the limits from causality.