A dual approach to quantum fluctuations in frustrated lattice spin models*

We develop a dual approach to describe quantum dynamics in lattice spin models, which allows us to describe nonperturbative \emph{quantum} trajectories in the spin path integral. The spin path integral takes the form of a combination of traces of ``dynamic density matrices'', which belong to either special linear group $SL(2,C)$ for a quantum ferromagnet or $SU(2)$ for an antiferromagnet. We analyze the latter model of a highly frustrated quantum antiferromagnet and find a class of non-perturbative trajectories that contribute to thermodynamics of the model at low temperatures.