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Functional-integral approach to Parisi-Wu stochastic quantization: Abelian gauge theory.

The method of Parisi and Wu of quantizing gauge theories (stochastic quantization) is reformulated using path integrals. We first review how the gauge fixing enters through the initial condition of the associated Langevin equation. We then prove, nonperturbatively, how the contribution of the Faddeev-Popov determinant is naturally generated by the Fokker-Planck dynamics without ever having to introduce it by hand. We restrict ourselves in this paper to Abelian gauge theories with nonlinear gauge fixing.