  In this paper, we first use semi-classical methods to study quantum field
theoretical aspects of the integrable noncommutative sine-Gordon model proposed
in [hep-th/0406065]. In particular, we examine the fluctuations at quadratic
order around the static kink solution using the background field method. We
derive equations of motion for the fluctuations and argue that at O(theta^2)
the spectrum of fluctuations remains essentially the same as that of the
corresponding commutative theory. We compute the one-loop two-point functions
of the sine-Gordon field and the additional scalar field present in the model
and exhibit logarithmic divergences, only some of which lead to UV/IR mixing.
We briefly discuss the one-loop renormalization in Euclidean signature and
comment on the obstacles in determining the noncommutativity corrections to the
quantum mass of the kink.
