Yang-Mills theory, 2+1 and 3+1 dimensions

Abstract

I review the analysis of (2+1)-dimensional Yang-Mills ($YM_{2+1})$ theory via the use of gauge-invariant matrix variables. The vacuum wavefunction, string tension, the propagator mass for gluons, its relation to the magnetic mass for $YM_{3+1}$ at nonzero temperature and the extension of our analysis to the Yang-Mills-Chern-Simons theory are discussed. A possible extension to 3+1 dimensions is also briefly considered.