  We generalize the idea of boundary states to the open string channel. They
describe emission and absorption of open strings in the presence of
intersecting D-branes. We construct the explicit oscillator representation for
the free boson and fermionic ghost. The inner product of such states describes
a disk amplitude of rectangular shape and possesses modular covariance with a
nontrivial conformal weight. We compare the result obtained here with those
obtained using two different methods, one employing the path integral formalism
and one employing the conformal anomaly. We find that all these methods give
consistent results. In our method, we must be careful in our treatment of the
singularity of the CFT near the corners. Specifically, we derive the correction
to the conformal weight of the primary field inserted at the corner, and it
gives the modular weight of the rectangle amplitude. We also carry out explicit
computations of the correlation functions.
