Schwinger and statistical physics: A spin-off success story and some challenging sequels

Some of the influences Julian Schwinger has had on condensed matter physics are discussed. The first part rapidly summarizes the language and methods he introduced to describe physical systems exactly and to approximate their properties systematically. The significance of these methods and the ways in which they have been extended are noted. The second part describes how these concepts have been applied to the condensed Bose fluid (i.e., helium 4), a system with rich and varied properties. Some fundamental features of this system are summarized. The third part examines recent advances in our understanding of helium at its critical point in three dimensions and below the critical point in two. A final section describes briefly certain features of chaotic behavior and what is needed to explain them. The problems encountered in the study of turbulence and other chaotic phenomena are compared and contrasted with those arising in other areas of statistical physics. Throughout, the direct and indirect contributions Schwinger has made to condensed matter physics and the contributions condensed matter physics and field theory have made to one another are emphasized.