  We present a semiclassical treatment of one-dimensional many-body quantum
systems in equilibrium, where quantum corrections to the classical field
approximation are systematically included by a renormalization of the classical
field parameters. Our semiclassical approximation is reliable in the limit of
weak interactions and high temperatures. As a specific example, we apply our
method to the interacting Bose gas and study experimentally observable
quantities, such as correlation functions of bosonic fields and the full
counting statistics of the number of particles in an interval. Where possible,
our method is checked against exact results derived from integrability, showing
excellent agreement.
