Infrared degrees of freedom of Yang-Mills theory in the Schroedinger representation

Abstract

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.