  The large-distance dynamics in quarkonium systems is investigated, in the
large N limit, through the saturation of Wilson loop averages by minimal
surfaces. Using a representation for the quark propagator in the presence of
the external gluon field based on the use of path-ordered phase factors, a
covariant three-dimensional bound state equation of the Breit-Salpeter type is
derived, in which the interaction potentials are provided by the
energy-momentum vector of the straight segment joining the quark to the
antiquark and carrying a constant linear energy density, equal to the string
tension. The interaction potentials are confining and reduce to the linear
vector potential in the static case and receive, for moving quarks,
contributions from the moments of inertia of the straight segment. The
self-energy parts of the quark propagators induce spontaneous breakdown of
chiral symmetry with a mechanism identical to that of the exchange of one
Coulomb-gluon. The nonrelativistic and ultrarelativistic properties of the
bound state spectrum are studied.
