Dynamics of interacting particle systems: stochastic process and field theory

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.