The boundary sine-Gordon theory: Classical and semi-classical analysis Original Research Article

We consider the sine-Gordon model on a half-line, with an additional potential term of the form −M cos[12β(ϕ − ϕ0)] at the boundary. We compute the classical time delay for general values of M, β and ϕ0 using τ-function methods and show that in the classical limit the method of images still works, despite the non-linearity of the problem. We also perform a semi-classical analysis, and find agreement with the exact quantum S-matrix conjectured by Ghoshal and Zamolodchikov.