  A continuous sequence of infinitesimal unitary transformations is used to
diagonalize the quantum sine-Gordon model for \beta^2\in(2\pi,\infty). This
approach can be understood as an extension of perturbative scaling theory since
it links weak- to strong-coupling behavior in a systematic expansion: a small
expansion parameter is identified and this parameter remains small throughout
the entire flow unlike the diverging running coupling constant of perturbative
scaling. Our approximation consists in neglecting higher orders in this small
parameter. We find very accurate results for the single-particle/hole spectrum
in the strong-coupling phase and can describe the full crossover from weak to
strong-coupling. The integrable structure of the sine-Gordon model is not used
in our approach. Our new method should be of interest for the investigation of
nonintegrable perturbations and for other strong-coupling problems.
