Renormalization-group study of field-theoretic<i>A</i>+<i>A</i>→0/

Abstract

We study field-theoretic A+A\ensuremath{\rightarrow}0/ in a perturbative renormalization-group framework. We calculate the reacted fraction and it is shown that, in addition to the reaction coupling constant, a second ``crossover'' parameter must be treated to all orders to obtain meaningful long-time results for spatial dimensions d\ensuremath{\le}2. At d=2 the result is consistent with known rigorous long-time bounds, but the short-time behavior remains inconsistent (trivial) analogously to the Landau ghost of QED and ${\mathrm{\ensuremath{\varphi}}}^{4}$ theory. We argue that this inconsistency is true to all orders in the coupling constants.