The classical sine-Gordon model is a two-dimensional integrable field theory,
with particle like solutions the so-called solitons. Using its integrability
one can define its quantum version without the process of canonical
quantization. This bootstrap method uses the fundamental propterties of the
model and its quantum features in order to restrict the structure of the
scattering matrix as far as possible. The classical model can be extended with
integrable discontinuities, purely transmitting jump-defects. Then the quantum
version of the extended model can be determined via the bootstrap method again.
But the outcoming quantum theory contains the so-called CDD uncertainity. The
aim of this article is to carry throw the semiclassical approximation in both
the classical and the quantum side of the defect sine-Gordon theory. The CDD
ambiguity can be restricted by comparing the two results. The relation between
the classical and quantum parameters as well as the resoncances appeared in the
spectrum are other objectives
