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In non-Abelian lattice gauge theories, the GaussVlaw constraint is solved, enabling gauge-invariant local dynamics. For the 2 + 1, SU(2) case, the result is a quantum theory of a discretized membrane. Further, this is equivalent to a theory of integer-valued scalars with derivative interactions and a "dual" gauge invariance. This is the dual form of 2+ 1, SU(2) gauge theory.

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We make a numerical study of the finite temperature properties of the SO(3) lattice gauge theory. As its symmetry properties are quite different from those of the SU (2) LGT, a different set of observables has to be considered in this model. We study several observables, such as the plaquette square, the Z(2) monopole density, the fundamental and adjoint Wilson line, and the tiled Wilson line correlation function. Our simulations show that the Z(2) monopoles condense at strong coupling just as in the bulk system. This transition is seen at approximately the same location as in the bulk system. A surprising observation is the multiple valuedness of the adjoint Wilson line at high temperatures. At high temperatures, we observe long lived metastable states in which the adjoint Wilson line takes positive and negative values. The numerical values of other observables in these two states appear to be almost the same. We study these states using different methods and also make comparisons with the high temperature behavior of the SU (2) LGT. Finally, we discuss various interpretations of our results and point out their relevance for the phase diagram of the SO (3) LGT at finite temperature.