Semiclassical quantization of the complex sine-Gordon field theory

The complex sine-Gordon model, a classically integrable field theory which exhibits highly nontrivial renormalization properties, is quantized semiclassically. The classical multisoliton solutions are derived by the inverse scattering method. The semiclassical mass spectrum is obtained from these results by computing the small-fluctuation determinant around the one-soliton solution. Dimensional regularization is used here. The particle spectrum turns out to be constituted by bound states of fundamental particles of like charge. Finally, the semiclassical $S$ matrix is calculated and crossing symmetry is exhibited.