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Quantum and classical integrable sine-Gordon model with defect. (English) Zbl 1219.81189
Summary: Defects which are predominant in a realistic model, usually spoil its integrability or solvability. We on the other hand show the exact integrability of a known sine-Gordon field model with a defect (DSG), at the classical as well as at the quantum level based on the Yang-Baxter equation. We find the associated classical and quantum $$R$$-matrices and the underlying q-algebraic structures, analyzing the exact lattice regularized model. We derive algorithmically all higher conserved quantities $$C_n$$, $$n=1,2,\dots$$, of this integrable DSG model, focusing explicitly on the contribution of the defect point to each $$C_n$$. The bridging condition across the defect, defined through the Bäcklund transformation is found to induce creation or annihilation of a soliton by the defect point or its preservation with a phase shift.

##### MSC:
 81T10 Model quantum field theories 81R12 Groups and algebras in quantum theory and relations with integrable systems
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##### References:
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