Quantum energy inequalities and stability conditions in quantum field theory

Abstract

Quantum Energy Inequalities (QEIs) are constraints on the extent to which quantum fields can violate the energy conditions of classical general relativity. As such they are closely related to the gravitational stability of quantised matter. In this contribution we discuss links between QEIs and other stability conditions in quantum field theory: the microlocal spectrum condition, passivity and nuclearity. The fist two links suggest an interconnection between stability conditions at three different length scales, while the third hints at a deeper origin of QEIs.