  We investigate three different methods to tackle the problem of
diffusion-limited reactions (annihilation) of hard-core classical particles in
one dimension. We first extend an approach devised by Lushnikov and calculate
for a single species the asymptotic long-time and/or large distance behavior of
the two-point correlation function. Based on a work by Grynberg et al., which
was developed to treat stochastic adsorption-desorption models, we provide in a
second step the exact two-point correlation function (both for one and
two-time) of Lushnikov's model. We then propose a new formulation of the
problem in terms of path integrals for pseudo-fermions. This formalism can be
used to advantage in the multi-species case, specially when applying
perturbative renormalization group techniques.
