Lüscher's μ-term and finite volume bootstrap principle for scattering states and form factors

We study the leading order finite size correction (Lüscher's μ-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 μ-term is intimately connected to the inner structure of the particles, i.e., 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 μ-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 μ-term, but also provides the sum over a subset of higher order corrections as well.