Abstract
A variational study is made of the vacuum state of the SU 2 lattice gauge theory, with and without fermions, in 2 + 1 space-time dimensions. The vacuum of the pure gauge theory is modelled using a variational state proposed by Arisue, Kato and Fujiwara. The static interquark potential in this medium is studied. It is found that the behaviour of these potentials at intermediate coupling is improved by the nontrivial vacuum; for example, there is greater rotational symmetry when the gluon condensate is present. A condensate of massless fermions is then added to the state, and another variational calculation is performed. The resulting approximation to the vacuum state is noticeably different from that obtained in the pure gauge case. It is argued that in order to bring about the correct scaling behaviour for the gluon and (especially) the fermion condensates, it will be necessary to include widely separated q q pairs in the state.
Published Version
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