The boundary sine-Gordon theory: classical and semi-classical analysis

Abstract

We consider the sine-Gordon model on a half-line, with an additional potential term of the form $-M\cos \frac{\beta }{2}(\phi -{\phi }_0)$ at the boundary. We compute the classical time delay for general values of $M$, $\beta$ and ${\phi }_0$ using $\tau$-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.

19 pages, 5 figures. Preprint USC-94-013. (Numerical mistake corrected.)

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