  The emergence of a finite staggered magnetization in quantum Heisenberg
antiferromagnets subject to a uniform magnetic field can be viewed as
Bose-Einstein condensation of magnons. Using non-perturbative results for the
infrared behavior of the interacting Bose gas, we present exact results for the
staggered spin-spin correlation functions of quantum antiferromagnets in a
magnetic field at zero temperature. In particular, we show that in dimensions 1
< D <= 3 the longitudinal dynamic structure factor S_parallel(q,omega)
describing staggered spin fluctuations in the direction of the staggered
magnetization exhibits a critical continuum whose weight can be controlled
experimentally by varying the magnetic field.
