On the absence of simultaneous reflection and transmission in integrable impurity systems

Details On the absence of simultaneous reflection and transmission in integrable impurity systems On the absence of simultaneous reflection and transmission in integrable impurity systems

2002-01-18

arxiv.org/abs/hep-th/0201142v3

Physics

High Energy Physics

High Energy Physics - Theory

11 pages Latex, 3 figures, clarifying remarks added

Scientific paper

We establish that the Yang-Baxter equations in the presence of an impurity can in general only admit solutions of simultaneous tranmission and reflection when the transmission and reflection amplitudes commute in the defect degrees of freedom with an additional exchange of the corresponding rapidities. In the absence of defect degrees of freedom we show in complete generality, that the only exceptions to this are theories which possess rapidity independent bulk scattering matrices. In particular bulk theories with diagonal scattering matrices, can only be the free Boson and Fermion, the Federbush model and their generalizations. These anyonic solutions do not admit the possibility of excited impurity states.

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