The new method based on the operator formalism proposed by Abe and Nakanishi
is applied to the quantum nonlinear abelian gauge theory in two dimension. The
soluble models in this method are extended to wider class of quantum field
theories. We obtain the exact solution in the canonical-quantization operator
formalism in the Heisenberg picture. So this analysis might shed some light on
the analysis of gravitational theory and non-polynomial field theories.Comment: LaTeX, 12 pages, to be published in IJMP