Quantum energy inequalities for conformal fields

A surprising property of quantum fields is that their local energy densities need not be positive (and are in fact unbounded from below as a function of the quantum state). In principle, negative energy densities, especially when coupled to gravity, permit many pathological phenomena: it is therefore important to place constraints on their magnitude and duration. This talk will describe bounds on negative energy densities known as Quantum Energy Inequalities (QEIs) and some of their applications.

A variety of QEIs have been proved for free quantum fields. This talk will present the first examples of QEIs to be established for interacting quantum fields, namely for a class of two-dimensional conformal field theories (joint work with S Hollands). In addition, analogues of QEIs in quantum mechanics will be described (joint work with SP Eveson & R Verch).