  We show that it is in principle possible to construct dualities between
commutative and non-commutative theories in a systematic way. This construction
exploits a generalization of the exact renormalization group equation (ERG). We
apply this to the simple case of the Landau problem and then generalize it to
the free and interacting non-canonical scalar field theory. This constructive
approach offers the advantage of tracking the implementation of the Lorentz
symmetry in the non-commutative dual theory. In principle, it allows for the
construction of completely consistent non-commutative and non-local theories
where the Lorentz symmetry and unitarity are still respected, but may be
implemented in a highly non-trivial and non-local manner.
