Infinite dimension reflection matrices in the sine-Gordon model with a boundary

Using the sine-Gordon model as the prime example an alternative approach to integrable boundary conditions for a theory restricted to a half-line is proposed. The main idea is to explore the consequences of taking into account the topological charge residing on the boundary and the fact it changes as solitons in the bulk reflect from the boundary. In this context, reflection matrices are intrinsically infinite dimensional, more general than the two-parameter Ghoshal-Zamolodchikov reflection matrix, and related in an intimate manner with defects.