Abstract

In 1975, Lieb and Thirring gave an elegant and useful combination of the uncertainty and the exclusion principles of quantum mechanics, proving a lower bound for the kinetic energy of a fermionic many-particle wave function in terms of its local particle density. Together with J. P. Solovej, we have extended such a bound to apply to more general identical particles, whose quantum statistics can be modeled using bosons with a local repulsive interaction, such as anyons in two dimensions. In this talk I consider the generalization and application of similar energy bounds to a large family of pair-interacting Bose gases, including some recent work with P. T. Nam and F. Portmann concerning the relativistic case.