  In previous work [cond-mat/9904207,cond-mat/9904215] we have developed a
general method for casting stochastic partial differential equations (SPDEs)
into a functional integral formalism, and have derived the one-loop effective
potential for these systems. In this paper we apply the same formalism to a
specific field theory of considerable interest, the reaction-diffusion-decay
system. When this field theory is subject to white noise we can calculate the
one-loop effective potential (for arbitrary polynomial reaction kinetics) and
show that it is one-loop ultraviolet renormalizable in 1, 2, and 3 space
dimensions. For specific choices of interaction terms the one-loop
renormalizability can be extended to higher dimensions. We also show how to
include the effects of fluctuations in the study of pattern formation away from
equilibrium, and conclude that noise affects the stability of the system in a
way which is calculable.
