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 {ital M}{sub {ital A}}{sup 2}{ital a2}=5.29(30){times}10{sup 2}{ital g{minus}2}exp({minus}5.42(6)/{ital g}{sup 2}), and the ratio of the symmetric mass gap ({ital M}{sub {ital S}}) to the antisymmetric mass gap ({ital M}{sub {ital A}}) is {ital M}{sub {ital S}}/{ital M}{sub {ital A}}=2.2(3). For the SU(2) model, the scaling behavior of the symmetric mass gap is {ital M}{sub {ital S}}{sup {ital a}}=2.22(5){ital g}{sup 2}{minus}0.38(4){ital g}{sup 4}. These results are in good agreement with theoretical expectations.