  Yang-Mills theories in 2+1 (or 3) dimensions are interesting as nontrivial
gauge theories in their own right and as effective theories of QCD at high
temperatures. I shall review the basics of our Hamiltonian approach to this
theory, emphasizing symmetries with a short update on its status. We will show
that the calculation of the vacuum wave function for Yang-Mills theory in 2+1
dimensions is in the lowest order of a systematic expansion. Expectation values
of observables can be calculated using an effective interacting chiral boson
theory, which also leads to a natural expansion as a double series in the
coupling constant (to be interpreted within a resummed perturbation series) and
a particular kinematical factor. The calculation of the first set of
corrections in this expansion shows that the string tension is modified by
about -0.3% to -2.8% compared to the lowest order value. This is in good
agreement with lattice estimates.
