  We reexamine the 1/S-correction to the self-energy of the gapless magnon of a
D-dimensional quantum Heisenberg antiferromagnet in a uniform magnetic field h
using a hybrid approach between 1/S-expansion and non-linear sigma model, where
the Holstein-Primakoff bosons are expressed in terms of Hermitian field
operators representing the uniform and the staggered components of the
spin-operators [N. Hasselmann and P. Kopietz, Europhys. Lett. {\bf{74}}, 1067
(2006)]. By integrating over the field associated with the uniform
spin-fluctuations we obtain the effective action for the staggered
spin-fluctuations on the lattice, which contains fluctuations on all length
scales and does not have the cutoff ambiguities of the non-linear sigma model.
We show that in dimensions D <= 3 the magnetic field dependence of the
spin-wave velocity c(h) is non-analytic in h^2, with c(h) - c(0) proportional
to h^2 \ln | h | in D=3, and c(h) - c(0) proportional to | h | in D=2. The
frequency dependent magnon self-energy is found to exhibit an even more
singular magnetic field dependence, implying a strong momentum dependence of
the quasi-particle residue of the gapless magnon. We also discuss the problem
of spontaneous magnon decay and show that in D > 1 dimensions the damping of
magnons with momentum k is proportional to |k|^{2D -1} if spontaneous magnon
decay is kinematically allowed.
