  Bound state poles in the $S$-matrix of perturbative QED are generated by the
{\em divergence} of the expansion in $\alpha$. The perturbative corrections are
necessarily singular when expanding around free, \order{\alpha^0} $in$ and
$out$ states that have no overlap with finite-sized atomic wave functions.
Nevertheless, measurables such as binding energies do have well-behaved
expansions in powers of $\alpha$ (and $\log\alpha$).
  It is desirable to formulate the concept of "lowest order" for gauge theory
bound states such that higher order corrections vanish in the $\alpha \to 0$
limit. This may allow to determine a lowest order term for QCD hadrons which
incorporates essential features such as confinement and chiral symmetry
breaking, and thus can serve as the starting point of a useful perturbative
expansion.
  I discuss a "Born" (no loop, lowest order in $\hbar$) approximation. Born
level states are bound by gauge fields which satisfy the classical field
equations. Gauss' law determines a distinct field $A^0(\xv)$ for each
instantaneous position of the charges. A Poincar\'e covariant boundary
condition for the gluon field leads to a confining potential for $q\bar q$ and
$qqq$ states. In frames where the bound state is in motion the classical gauge
field is obtained by a Lorentz boost of the rest frame field.
