Renormalization group approach to reaction-diffusion systems with input particles

We consider reaction-diffusion systems of a single species (A + A --> phi) in the absence and the presence of a particle input. Applying renormalizati on group theory to a field theoretic description and matching theory to the renormalization group trajectory integrals of the systems, we find that fo r d < 2 in the absence of an input, the density decays as c(t) similar to t (-nu) with the dynamic exponent nu = d/2 and in the presence of input the d ensity grows as c(I) similar to I-mu with the static exponent mu = d/(d + 2 ), while for d > 2 the behaviors are mean-field like and for d = 2 there ar e logarithmic corrections to the mean-field results. The results for the ab sence of input are consistent with the previous results obtained using diff erent methods. In addition, we propose a rigorous proof of Racz's conjectur e about the relation between the static and the dynamic exponents, mu = nu/ (1 + nu).