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

Abstract

I review the analysis of (2+1)-dimensional Yang-Mills (YM2+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 YM3+1at 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.