Quantum Energy Inequality for the Massive Ising Model

TL;DR

This paper establishes a quantum energy inequality for the massive Ising model, providing a fundamental lower bound on energy density averages in an interacting quantum field theory with a nontrivial S-matrix.

Contribution

It is the first QEI derived for an interacting quantum field theory with a nontrivial S-matrix, revealing properties of energy densities in the massive Ising model.

Findings

Existence of locally negative energy densities in one-particle states

Energy density operator is non-additive for multi-particle states

First QEI established for an interacting quantum field theory

Abstract

A Quantum Energy Inequality (QEI) is derived for the massive Ising model, giving a state-independent lower bound on suitable averages of the energy density; the first QEI to be established for an interacting quantum field theory with nontrivial S-matrix. It is shown that the Ising model has one-particle states with locally negative energy densities, and that the energy density operator is not additive with respect to combination of one-particle states into multi-particle configurations.