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In this work we propose an action to describe diffusion limited chemicalreactions belonging to various classes of universality. This action is treatedthrough Thompson's approach and can encompass both cases where we havesegregation as in the $A+B\to 0$ reaction, as well the simplest one, namely the$A+A\to 0$ reaction .Our results for long time and long wavelength behaviors ofthe species concentrations and reaction rates agree with exact results ofPeliti for $A+A\to 0$ reaction and rigorous results of Bramson and Lebowitz for$A+B\to 0$ reaction, with equal initial concentrations.The different classes ofuniversality are reflected by the obtained upper critical dimensions varyingcontinuously from $d_{c}=2$ in the first case to $d_{c}=4$ in the last one.Just at the upper critical dimensions we find universal logarithmic correctionsto the mean field behavior.

UNIFIED TREATMENT OF A+B→0 AND A+A→0 CHEMICAL REACTIONS THROUGH THOMPSON'S APPROACH