  For temperatures below 0.6 K the geometrically frustrated layered quantum
antiferromagnet Cs$_2$CuCl$_4$ in a magnetic field perpendicular to the layers
orders magnetically in a so-called cone state, where the magnetic moments have
a finite component in the field direction while their projection onto the
layers forms a spiral. Modeling this system by a two-dimensional spatially
anisotropic quantum Heisenberg antiferromagnet with Dzyaloshinskii-Moriya
interaction, we find that even for vanishing temperature the usual spin-wave
expansion is plagued by infrared divergencies which are due to the coupling
between longitudinal and transverse spin fluctuations in the cone state.
Similar divergencies appear also in the ground state of the interacting Bose
gas in two and three dimensions. Using known results for the correlation
functions of the interacting Bose gas, we present a non-perturbative expression
for the dynamic structure factor in the cone state of Cs$_2$CuCl$_4$. We show
that in this state the spectral line shape of spin fluctuations exhibits
singular scattering continua which can be understood in terms of the well-known
anomalous longitudinal fluctuations in the ground state of the two-dimensional
Bose gas.
