Gauge theory of two-dimensional spin- Heisenberg antiferromagnet

A gauge theory of the spin- Heisenberg antiferromagnet (HA) on a two-dimensional square lattice is developed, which is based on the diagonal G_D of the group product SO(3)×SU(2). For classical gauge fields G_D is homeomorphic to SO(3). The structure of the theory is such that the quantum spin- field propagates on the background gauge field. For special gauges the excitations of the spin-field are computed and compared to the excitations of the O(3) σ model for the same gauge. The significance of negative excitational modes with respect to a semiclassical actionГ_sc of the spin- HA is discussed. Some properties ofГ_sc represented as a chiral SO(3) model in a continuum representation are worked out.