The qualitative behavior of Yang-Mills theory in 2 + 1 dimensions

The SU(2) gauge theory of gluons (no quarks) is studied in two space and one time dimensions. Only qualitative or suggestive discussions are made. Starting from the quantum field equations it is argued that the necessary gauge invariance of the wave functional results, in this non-abelian case, in a finite energy for any excitation (“glueball”) above the ground state. Furthermore, fluctuations in which gauging factors change sign can occur independently in regions adequately separated in space. This results in a potential between distant massive quarks rising linearly with distance (quark confinement). The situation in 3 + 1 dimensions is not discussed.