Some aspects of jump-defects in the quantum sine-Gordon model

The classical sine-Gordon model permits integrable discontinuities, orjump-defects, where the conditions relating the fields on either side of adefect are Backlund transformations frozen at the defect location. The purposeof this article is to explore the extent to which this idea may be extended tothe quantum sine-Gordon model and how the striking features of the classicalmodel may translate to the quantum version. Assuming a positive defectparameter there are two types of defect. One type, carrying even charge, isstable, but the other type, carrying odd charge, is unstable and may beconsidered as a resonant bound state of a soliton and a stable defect. Thescattering of solitons with defects is considered in detail, as is thescattering of breathers, and in all cases the jump-defect is purelytransmitting. One surprising discovery concerns the lightest breather. Itstransmission factor is independent of the bulk coupling - a propertysusceptible to a perturbative check, but not shared with any of the otherbreathers. It is argued that classical jump-defects can move and some commentsare made concerning their quantum scattering matrix.Comment: 33 pages; a few typos have been corrected and two references adde