  These lecture notes focus on the bound state sector of QCD. Motivated by data
which suggests that the strong coupling \alpha_s(Q) freezes at low Q, and by
similarities between the spectra of hadrons and atoms, I discuss if and how QCD
bound states may be treated perturbatively. I recall the basic principles of
perturbative gauge theory bound states at lowest order in the \hbar expansion.
Born level amplitudes are insensitive to the i\epsilon prescription of
propagators, which allows to eliminate the Z-diagrams of relativistic,
time-ordered Coulomb interactions. The Dirac wave function thus describes a
single electron which propagates forward in time only, even though the bound
state has any number of pair constituents when Feynman propagators are used. In
the absence of an external potential, states that are bound by the Coulomb
attraction of their constituents can be analogously described using only their
valence degrees of freedom. The instantaneous A^0 field is determined by Gauss'
law for each wave function component, i.e., for each position of the valence
constituents. Solutions for A^0 obtained with a boundary condition that imposes
an asymptotically constant energy density give rise to a linear potential for
color singlet q\bar q and qqq states. The strength of the linear potential is
determined by the boundary condition and is of lower order in \alpha_s than the
gluon exchange interaction, which may then be treated as a higher order
perturbative correction. Bound states evaluated to a given order in \alpha_s
and \hbar must have the full symmetry of the exact theory, including the
dynamic boost invariance of states quantized at equal time. The wave functions
are indeed found to have such a hidden invariance, which ensures the correct
dependence of the energy eigenvalues on the center of mass momentum. Thus
relativistic bound states can be studied using perturbative methods.
