  The massless bosonic field compactified on the circle of rational $R^2$ is
reexamined in the presense of boundaries. A particular class of models
corresponding to $R^2=\frac{1}{2k}$ is distinguished by demanding the existence
of a consistent set of Newmann boundary states. The boundary states are
constructed explicitly for these models and the fusion rules are derived from
them. These are the ones prescribed by the Verlinde formula from the S-matrix
of the theory. In addition, the extended symmetry algebra of these theories is
constructed which is responsible for the rationality of these theories.
Finally, the chiral space of these models is shown to split into a direct sum
of irreducible modules of the extended symmetry algebra.
