The classical sine-Gordon model permits integrable discontinuities, or jump-defects, where the conditions relating the fields on either side of a defect are Bäcklund transformations frozen at the defect location. The purpose of this article is to explore the extent to which this idea may be extended to the quantum sine-Gordon model and how the striking features of the classical model may translate to the quantum version. Assuming a positive defect parameter there are two types of defect. One type, carrying even charge, is stable, but the other type, carrying odd charge, is unstable and may be considered as a resonant bound state of a soliton and a stable defect. The scattering of solitons with defects is considered in detail, as is the scattering of breathers, and in all cases the jump-defect is purely transmitting. One surprising discovery concerns the lightest breather. Its transmission factor is independent of the bulk coupling — a property susceptible to a perturbative check, but not shared with any of the other breathers. It is argued that classical jump-defects can move and some comments are made concerning their quantum scattering matrix.
Bowcock, P., Corrigan, E., & Zambon, C. (2005). Some aspects of jump-defects in the quantum sine-Gordon model. Journal of High Energy Physics, 2005(08), Article 023. https://doi.org/10.1088/1126-6708/2005/08/023