  We construct exact duality transformations in pure SU(N) Hamiltonian lattice
gauge theory in (2+1) dimension. This duality is obtained by making a series of
iterative canonical transformations on the SU(N) electric vector fields and
their conjugate magnetic vector potentials on the four links around every
plaquette. The resulting dual description is in terms of the magnetic scalar
fields or plaquette flux loops and their conjugate electric scalar potentials.
Under SU(N) gauge transformations they both transform like adjoint matter
fields. The dual Hamiltonian describes the nonlocal self-interactions of these
plaquette flux loops in terms of the electric scalar potentials and with
inverted coupling. We show that these nonlocal loop interactions can be made
local and converted into minimal couplings by introducing SU(N) auxiliary gauge
fields along with new plaquette constraints. The matter fields can be included
through minimal coupling. The techniques can be easily generalized to (3+1)
dimensions.
