Field-Theoretic Formulation of a Mode-Coupling Equation for Colloids

The only available quantitative description of the slowing down of the dynamics upon approaching the glass transition has been, so far, the mode-coupling theory, developed in the 1980s by Gotze and collaborators. The standard derivation of this theory does not result from a systematic expansion. We present a field-theoretic formulation that arrives at very similar mode-coupling equation but which is based on a variational principle and on a controlled expansion in a small dimensionless parameter. Our approach applies to such physical systems as colloids interacting via a mildly repulsive potential. It can in principle, with moderate efforts, be extended to higher orders and to multipoint correlation functions.