Root Systems and Boundary Bootstrap

Details Root Systems and Boundary Bootstrap Root Systems and Boundary Bootstrap

1996-03-16

arxiv.org/abs/hep-th/9603111v1

Physics

High Energy Physics

High Energy Physics - Theory

8 pages, latex file

Scientific paper

The principle of boundary bootstrap plays a significant role in the algebraic study of the purely elastic boundary reflection matrix $K_a(\theta)$ for integrable quantum field theory defined on a space-time with a boundary. However, general structure of that principle in the form as was originally introduced by Fring and K\"oberle has remained unclear. In terms of a new matrix $J_a(\theta)=\sqrt{K_a(\theta)/K_{\bar{a}}(i\pi +\theta)}$, the boundary bootstrap takes a simple form. Incidentally, a hypothesised expression of the boundary reflection matrix for simply-laced $ADE$ affine Toda field theory defined on a half line with the Neumann boundary condition is obtained in terms of geometrical quantities of root systems \`a la Dorey.

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