  We set up a new calculational framework for the Yang-Mills vacuum transition
amplitude in the Schroedinger representation. After integrating out hard-mode
contributions perturbatively, we perform a gauge invariant gradient expansion
of the ensuing soft mode action which renders a subsequent saddle point
expansion for the vacuum overlap manageable. The standard "squeezed"
approximation for the vacuum wave functional then allows for an essentially
analytical treatment of physical amplitudes. Moreover, it leads to the
identification of dominant and gauge invariant classes of gauge field orbits
which play the role of gluonic infrared (IR) degrees of freedom. Those emerge
as a rich variety of (mostly solitonic) solutions to the saddle point equations
which are characterized by a common relative gauge orientation of the
underlying gluon fields. We discuss their scale stability, guaranteed by a
virial theorem, and other general properties including topological quantum
numbers and action bounds. We then find important saddle point solutions
explicitly and examine their physical impact. Some of them are related to
tunneling solutions of the classical Yang-Mills equation, i.e. to instantons
and merons, while others appear to play unprecedented roles. A remarkable new
class of IR degrees of freedom comprises vortex and knot solutions of
Faddeev-Niemi type, potentially related to glueballs.
