Exact solution of a massless scalar field with a relevant boundary interaction

Details Exact solution of a massless scalar field with a relevant boundary interaction Exact solution of a massless scalar field with a relevant boundary interaction

1994-06-18

arxiv.org/abs/hep-th/9406125v1

Nucl.Phys. B430 (1994) 577-596

Physics

High Energy Physics

High Energy Physics - Theory

23 pages, USC-94-10

Scientific paper

10.1016/0550-3213(94)90160-0

We solve exactly the "boundary sine-Gordon" system of a massless scalar field \phi with a \cos[\beta\phi/2] potential at a boundary. This model has appeared in several contexts, including tunneling between quantum-Hall edge states and in dissipative quantum mechanics. For \beta^2 < 8\pi, this system exhibits a boundary renormalization-group flow from Neumann to Dirichlet boundary conditions. By taking the massless limit of the sine-Gordon model with boundary potential, we find the exact S matrix for particles scattering off the boundary. Using the thermodynamic Bethe ansatz, we calculate the boundary entropy along the entire flow. We show how these particles correspond to wave packets in the classical Klein-Gordon equation, thus giving a more precise explanation of scattering in a massless theory.

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