Quantum energy inequalities in integrable quantum field theories

TL;DR

This paper constructs local energy density candidates in integrable quantum field theories, establishing bounds and uniqueness conditions at the one-particle level based on fundamental principles.

Contribution

It introduces a method to determine the energy density form in integrable models from first principles and proves lower bounds for local energy averages.

Findings

Energy density form fixed up to polynomial in energy.

Existence of lower bounds for local energy density averages.

Uniqueness of energy density form in specific models.

Abstract

In a large class of factorizing scattering models, we construct candidates for the local energy density on the one-particle level starting from first principles, namely from the abstract properties of the energy density. We find that the form of the energy density at one-particle level can be fixed up to a polynomial function of energy. On the level of one-particle states, we also prove the existence of lower bounds for local averages of the energy density, and show that such inequalities can fix the form of the energy density uniquely in certain models.