Series analysis of U(1) and SU(2) lattice gauge theory in 2+1 dimensions

Extended strong-coupling perturbation series are calculated for the vacuum energy and mass gaps of the U(1) and SU(2) lattice gauge theories in 2+1 dimensions. Extrapolating these series to the weak-coupling region, we estimate the scaling behavior for the antisymmetric mass gap of the U(1) model as $M_A^2{a}^2=5.29\mathrm{}\left(30\right)\mathrm{}\times {10}^2{g}^{-2\mathrm{}}\exp \left[\frac{-5.42\mathrm{}\left(6\right)\mathrm{}}{g^2}\right]$, and the ratio of the symmetric mass gap ($M_S$) to the antisymmetric mass gap ($M_A$) is $\frac{M_S}{M_A}=2.2\mathrm{}\left(3\right)\mathrm{}$. For the SU(2) model, the scaling behavior of the symmetric mass gap is $M_{S}a=2.22\mathrm{}\left(5\right)\mathrm{}{g}^2-0.38\mathrm{}\left(4\right)\mathrm{}{g}^4$. These results are in good agreement with theoretical expectations.