  Working with well known models in $(2+1)D$ we discuss the physics behind the
deformation of the canonical structure of these theories. A new deformation is
constructed linking the massless scalar field theory with the self-dual theory.
This is the exact dual of the known deformation connecting the Maxwell theory
with the Maxwell-Chern-Simons theory. Duality is used to establish a web of
relations between the mentioned theories and a physical picture of the
deformation procedure is suggested.
