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

TL;DR

This paper investigates Luscher's mu-term corrections in 1+1 dimensional integrable models, linking finite size effects to particle structure and validating results with numerical data from E8 scattering theory.

Contribution

It introduces a method connecting the mu-term to particle composition via bootstrap and analytic continuation, improving finite volume correction calculations.

Findings

Derived leading mu-term for bound states using analytic continuation.

Validated theoretical predictions with numerical data from E8 scattering theory.

Showed that bound state quantization captures higher order corrections.

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.