Quantum Energy Inequalities

Abstract

Quantum Energy Inequalities (QEIs) are lower bounds on local averages of energy densities and related quantities in quantum field theory (QFT). They replace the classical energy conditions of classical general relativity. This chapter surveys the violation of classical energy conditions in QFT and the theory of QEIs. In particular, (a) the main properties of QEIs are indicated using the example of a free scalar field in Minkowski spacetime; (b) a rigorous derivation of a QEI for scalar fields in general curved spacetimes is given; (c) the resulting QEI is evaluated explicitly in some specific cases; (d) further recent developments, including QEIs for conformal field theories and an integrable QFT are presented, along with work on the probability distribution for measurements of averaged energy densities; (e) the status of QEIs in interacting models is discussed; (f) various applications of the QEIs are presented.