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We study the 1/N expansion of field theories in the stochastic quantization method of Parisi and Wu using the supersymmetric functional approach. This formulation provides a systematic procedure to implement the 1/N expansion which resembles the ones used in the equilibrium. The 1/N perturbation theory for the nonlinear sigma-model in two dimensions is worked out as an example.

Vacuum polarization effects are nonperturbatively incorporated into the photon propagator to eliminate the severe infrared problems characteristic of (2+1)-dimensional QED (${\mathrm{QED}}_{3}$). The theory is thus rephrased in terms of a massive vector boson whose mass is ${\mathit{e}}^{2}$/8\ensuremath{\pi}. Subsequently, it is shown that electron-electron bound states are possible on ${\mathrm{QED}}_{3}$.