Plaquette formulation and the Bianchi identity for lattice gauge theories

We extend Halpern's field-strength formulation and dual potentials (for continuum gauge theories) to abelian and non-abelian lattice gauge theories. New results include: (i) plaquette formulation of all lattice gauge theories, (ii) the strong coupling expansion is seen as (a) a perturbation in dual links or (b) a gradual restoration of the lattice Bianchi identity. To leading order in the strong coupling expansion the lattice Bianchi identity is completely ignored. Geometrical interpretation of the lattice Bianchi identity is presented along with a discussion of the “abelianization” of the non-abelian identity and its connection with gauge-invariant variables. For abelian theories we also show that the dual potential is Fourier conjugate to the Bianchi identity and that the Coulomb gas representation of these theories is easily obtained in this formulation.