  We present an approach to the dynamics of interacting particle systems, which
allows to derive path integral formulas from purely stochastic considerations.
We show that the resulting field theory is a dual version of the standard
theory of Doi and Peliti. This clarify both the origin of the Cole-Hopf map
between the two approaches and the occurence of imaginary noises in effective
Langevin equations for reaction-diffusion systems. The advantage of our
approach is that it focuses directly on the density field. We show some
applications, in particular on the Zero Range Process, hydrodynamic limits and
large deviation functional.
