Negative energy densities in integrable quantum field theories at one-particle level

TL;DR

This paper investigates negative energy densities in integrable quantum field theories, demonstrating their generic existence in one-particle states and establishing bounds that constrain the stress-energy tensor.

Contribution

It classifies the stress-energy tensor form in integrable models and shows how negative energy densities depend on model parameters, providing bounds and numerical analysis.

Findings

Negative energy densities exist in non-free integrable models.

Quantum energy inequalities impose bounds on energy density.

Negative energy density depends on coupling constants and model parameters.

Abstract

We study the phenomenon of negative energy densities in quantum field theories with self-interaction. Specifically, we consider a class of integrable models (including the sinh-Gordon model) in which we investigate the expectation value of the energy density in one-particle states. In this situation, we classify the possible form of the stress-energy tensor from first principles. We show that one-particle states with negative energy density generically exist in non-free situations, and we establish lower bounds for the energy density (quantum energy inequalities). Demanding that these inequalities hold reduces the ambiguity in the stress-energy tensor, in some situations fixing it uniquely. Numerical results for the lowest spectral value of the energy density allow us to demonstrate how negative energy densities depend on the coupling constant and on other model parameters.