  We present the systematic formalism to derive the path-integral formulation
for the hard-core particle systems far from equilibrium. Writing the master
equation for a stochastic process of the system in terms of the annihilation
and creation operators with the mixed commutation relations, we find the
Kramers-Moyal coefficients for the corresponding Fokker-Planck equation (FPE)
and the stochastic differential equation (SDE) is derived by connecting these
coefficients in the FPE to those in the SDE. Finally, the SDE is mapped onto
the field-theory using the path-integral, giving the field-theoretic action
which may be analyzed by the renormalization group method. We apply this
formalism to the two-species reaction-diffusion system with the drift, finding
a universal decay expoent for the long-time behavior of the average
concentration of particles in arbitrary dimensions.
