Abstract
The boundary reflection matrices for nonsimply laced affine Toda field theories defined on a half line with the Neumann boundary condition are investigated. The boundary reflection matrices for some pairs of the models are evaluated up to one loop order by perturbation theory. Then the exact boundary reflection matrices which are consistent with the one loop result are found under the assumption of ``duality'' and tested against algebraic consistency such as the boundary bootstrap equation and boundary crossing-unitarity relation. \textcopyright{} 1996 The American Physical Society.
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