Perturbative expansions for atoms in QED are developed around interacting
states, typically defined by the Schrödinger equation. Calculations are
nevertheless done using the standard Feynman diagram expansion around free
states. The classical $-\alpha/r$ potential is then obtained through an
infinite sum of ladder diagrams. The complexity of this approach may have
contributed to bound states being omitted from QFT textbooks, restricting the
field to select experts.
The confinement scale $\sim$ 1 fm of QCD must be introduced without changing the
Lagrangian. This can be done via a boundary condition on the gauge field, which
affects the bound state potential. The absence of confinement in Feynman
diagrams may be due to the free field boundary condition.
Poincaré invariance is realized dynamically for bound states, i.e., the
interactions are frame dependent. Gauge theories have instantaneous
interactions, due to gauge fixing at all points of space at the same time. In
bound state perturbation theory each order must have exact Poincaré
invariance. This is non-trivial even for atoms at lowest order.
I summarize a perturbative approach to equal time bound states in QED and
QCD, using a Fock expansion in temporal ($A^0=0$) gauge. The longitudinal
electric field $E_L$ is instantaneous and need not vanish at spatial infinity
for the constituents of color singlet states in QCD. Poincaré covariance
determines the boundary condition for $E_L$ up to a universal scale,
characterised by the gluon field energy density of the vacuum. A non-vanishing
density contributes a linear term to the $q\bar{q}$ potential, while $qqq,\
q\bar{q}g$ and $gg$ color singlet states get analogous confining potentials.

