  We study spin-wave interactions in quantum antiferromagnets by expressing the
usual magnon annihilation and creation operators in terms of Hermitian field
operators representing transverse staggered and ferromagnetic spin
fluctuations. In this parameterization, which was anticipated by Anderson in
1952, the two-body interaction vertex between staggered spin fluctuations
vanishes at long wavelengths. We derive a new effective action for the
staggered fluctuations only by tracing out the ferromagnetic fluctuations. To
one loop order, the renormalization group flow agrees with the
nonlinear-$\sigma$-model approach.
