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

HOW TO SOLVE QUANTUM NONLINEAR ABELIAN GAUGE THEORY IN TWO DIMENSIONS IN THE HEISENBERG PICTURE