  We consider frequency dependence of the neutron scattering amplitude from a
two-dimensional quantum antiferromagnet. It is well known that the long range
order disappears at any finite temperature and hence the elastic neutron
scattering Bragg peak is transformed to the quasielastic neutron scattering
spectrum ~dw/w. We show that the widely known formula for the spectrum of an
isotropic antiferromagnet derived by Auerbach and Arovas should be supplemented
by a logarithmic term that changes the integrated intensity by two times. A
similar formula for an easy-plane magnet is very much different because of the
Berezinsky-Kosterlitz-Thouless physics. An external uniform magnetic field
switches smoothly the isotropic magnet to the easy-plane magnet. We demonstrate
that the quasielastic neutron scattering spectrum in the crossover regime
combines properties of both limiting cases. We also consider a quantum
antiferromagnet close to the O(3) quantum critical point and show that in an
external uniform magnetic field the intensity of elastic (quasielastic) neutron
scattering peak depends linearly and significantly on the applied field.
