Quantum energy inequalities in integrable models with several particle species and bound states

TL;DR

This paper establishes quantum energy inequalities in integrable quantum field theories with multiple particle types and bound states, linking energy bounds to form factors and classifying stress-energy tensors.

Contribution

It provides the first state-independent QEIs for models with constant scattering and classifies stress-energy tensors in generic models, connecting QEIs to form factor asymptotics.

Findings

Proves a state-independent QEI for models with constant scattering functions.

Establishes a one-particle level QEI for generic integrable models.

Links the existence of QEIs to the asymptotic behavior of two-particle form factors.

Abstract

We investigate lower bounds to the time-smeared energy density, so-called quantum energy inequalities (QEI), in the class of integrable models of quantum field theory. Our main results are a state-independent QEI for models with constant scattering function and a QEI at one-particle level for generic models. In the latter case, we classify the possible form of the stress-energy tensor from first principles and establish a link between the existence of QEIs and the large-rapidity asymptotics of the two-particle form factor of the energy density. Concrete examples include the Bullough-Dodd, the Federbush, and the $O(n)$-nonlinear sigma models.