Feynman's Last Problem 30 years Later: Liquid Helium and QCD
City University, New York.
In 1954, Feynman gave a beautiful analysis of superfluid Helium using general properties of wave functions and of the space of particle configurations. In the 1970s, starting with the discovery of asymptotic freedom and the emergence of QCD, the question of quark confinement and the generation of a mass gap was recognized as an important question about the nonperturbative behavior of nonabelian gauge theories. Needless to say, this has proved to be a very difficult problem to analyze. Two spatial dimensions would provide the simplest case of a nontrivial Yang-Mills theory which could exhibit confinement and mass gap. In 198, Feynman tried to use a set of arguments similar to what he had developed for superfluidity to argue for the existence of a mass gap for these theories. Did he succeed? Did he fail? If so, to what extent? I shall give a brief recapitulation of Feynman's arguments for Helium and then present his arguments for YM(2+1), in a slightly modernized and more precise language, so that we may gain some perspective on how much progress has been made. The emphasis will be on concepts more than on detailed formulae.