  The $A + B\to 0$ diffusion-limited reaction, with equal initial densities
$a(0) = b(0) = n_0$, is studied by means of a field-theoretic renormalization
group formulation of the problem. For dimension $d > 2$ an effective theory is
derived, from which the density and correlation functions can be calculated. We
find the density decays in time as $a,b \sim C\sqrt{\D}(Dt)^{-d/4}$ for $d <
4$, with $\D = n_0-C^\prime n_0^{d/2} + \dots$, where $C$ is a universal
constant, and $C^\prime$ is non-universal. The calculation is extended to the
case of unequal diffusion constants $D_A \neq D_B$, resulting in a new
amplitude but the same exponent. For $d \le 2$ a controlled calculation is not
possible, but a heuristic argument is presented that the results above give at
least the leading term in an $\epsilon = 2-d$ expansion. Finally, we address
reaction zones formed in the steady-state by opposing currents of $A$ and $B$
particles, and derive scaling properties.
