L\"uscher-corrections for 1-particle form-factors in non-diagonally scattering integrable quantum field theories

TL;DR

This paper derives a generalized Lüscher formula for calculating finite-volume corrections to 1-particle form-factors in non-diagonally scattering integrable quantum field theories, extending previous results to more complex models.

Contribution

The authors develop a new Lüscher formula applicable to non-diagonally scattering theories, including fermions and operators with Lorentz-spin, validated in the Massive Thirring Model.

Findings

Derived a Lüscher formula for non-diagonal scattering

Validated the formula against 1-loop perturbation theory

Extended applicability to fermions and spinful operators

Abstract

In this paper we derive from field theory a L\"uscher-formula, which gives the leading exponentially small in volume corrections to the 1-particle form-factors in non-diagonally scattering integrable quantum field theories. Our final formula is expressed in terms of appropriate expressions of 1- and 3-particle form-factors, and can be considered as the generalization of previous results obtained for diagonally scattering bosonic integrable quantum field theories. Since our formulas are also valid for fermions and operators with non-zero Lorentz-spin, we demonstrated our results in the Massive Thirring Model, and checked our formula against 1-loop perturbation theory finding perfect agreement.