  We consider theoretically the effects of an applied uniform magnetic field on
the magnetic spectrum of anisotropic two-dimensional and Dzyaloshinskii-Moriya
layered quantum Heisenberg antiferromagnets. The first case is relevant for
systems such as the two-dimensional square lattice antiferromagnet
Sr(2)CuO(2)Cl(2), while the later is known to be relevant to the physics of the
layered orthorhombic antiferromagnet La(2)CuO(4). We first establish the
correspondence betwenn the low-energy spectrum obtained within the anisotropic
non-linear sigma model and by means of the spin-wave approximation for a
standard easy-axis antiferromagent. Then, we focus on the field-theory approach
to calculate the magnetic field dependence of the magnon gaps and spectral
intensities for magnetic fields applied along the three possible
crystallographic directions. We discuss the various possible ground states and
their evolution with temperature for the different field orientations, and the
occurrence of spin-flop transitions for fields perpendicular to the layers
(transverse fields) as well as for fields along the easy axis (longitudinal
fields). Measurements of the one-magnon Raman spectrum in Sr(2)CuO(2)Cl(2) and
La(2)CuO(4) and a comparison between the experimental results and the
predictions of the present theory will be reported in part II of this research
work [L. Benfatto et al., cond-mat/0602664].
