Luscher's mu-term and finite volume bootstrap principle for scattering states and form factors

Abstract

We study the leading order finite size correction (Luscher's mu-term) associated to moving one-particle states, arbitrary scattering states and finite volume form factors in 1+1 dimensional integrable models. Our method is based on the idea that the mu-term is intimately connected to the inner structure of the particles, ie. their composition under the bootstrap program. We use an appropriate analytic continuation of the Bethe-Yang equations to quantize bound states in finite volume and obtain the leading mu-term (associated to symmetric particle fusions) by calculating the deviations from the predictions of the ordinary Bethe-Yang quantization. Our results are compared to numerical data of the E8 scattering theory obtained by truncated fermionic space approach. As a by-product it is shown that the bound state quantization does not only yield the correct mu-term, but also provides the sum over a subset of higher order corrections as well.

21 pages, 35 eps figures, LaTeX2e file

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