We have studied the instant form quantization and light front quantization of conformally gauge fixed polyakov D1 brane action with and without scalar dilation field and showed these theories when consider in the presence of background gauge fields such as the 2- form gauge field Bαβ(σ,τ) or in the presence of U(1) gauge field Aα(σ,τ) and constant scalar axion field C(σ,τ). The instant form quantization is studied in the equal world sheet time framework on hyperplanes defined by world σ o = τ = constant and light front quantization in equal light cone world sheet time framework in hyperplane defined by σ + = (τ+ σ) = constant. TheHamiltonformulation is given by two approaches: The first is Dirac approach while the second is Güler approach. The equal equations of motion are obtained as total differential equations in many variables. These equations of motion are in exact agreement with those equations that had been obtained using Dirac's method
