  We develop an analytical approach for studying lattice gauge theories within
the plaquette representation where the plaquette matrices play the role of the
fundamental degrees of freedom. We start from the original Batrouni formulation
and show how it can be modified in such a way that each non-abelian Bianchi
identity contains only two connectors instead of four. In addition, we include
dynamical fermions in the plaquette formulation. Using this representation we
construct the low-temperature perturbative expansion for U(1) and SU(N) models
and discuss its uniformity in the volume. The final aim of this study is to
give a mathematical background for working with non-abelian models in the
plaquette formulation.
