Lower bounds for the energy density in quantum integrable models

The energy density is positive in classical field theory, a property that fails to be true in the quantum regime. However, if it were indefinitely negative, this would conflict with the stability of spacetime. Fortunately, lower bounds exist and have been proved for free quantum field theory and conformal theories. We study, in a class of massive quantum integrable models, lower bounds for local averages of the energy density, establishing results for QFTs with self-interaction.