Unified treatment of A+B -> O and A+A -> O chemical reactions through Thompson's approach

In this work we propose an action to describe diffusion limited chemical re actions belonging to various classes of universality. This action is treate d through Thompson's approach and can encompass both cases where we have se gregation as in the A + B --> 0 reaction, as well as the simplest one, name ly the A + A --> 0 reaction. Our results for long-time and long-wavelength behaviors of the species concentrations and reaction rates agree with exact results of Peliti for A + A --> 0 reaction and rigorous results of Bramson and Lebowitz for A + B --> 0 reaction, with equal initial concentrations. The different classes of universality are reflected by the obtained upper c ritical dimensions varying continuously from d(c) = 2 in the first case to d(c) = 4 in the last one. Just as at the upper critical dimensions, we find universal logarithmic corrections to the mean field behavior.