Field strength formulation,lattice Bianchi identities and perturbation theory for non-Abelian models

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)$U(1)$ and SU(N)$\mathit{SU}(N)$ 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.