  We discuss the consequences of spin current conservation in systems with
SU(2) spin symmetry that is spontaneously broken by partial magnetic order,
using a momentum-space approach. The long-distance interaction is mediated by
Goldstone magnons, whose interaction is expressed in terms of the electron
Green's functions. There is also a Higgs mode, whose excitation energy can be
calculated. The case of fast magnons obeying linear dispersion relation in
three spatial dimensions admits nonperturbative treatment using the Gribov
equation, and the solution exhibits singular behaviour which has an
interpretation as a tower of spin-1 electronic excitations. This occurs near
the Mott insulator state. The electrons are more free in the case of slow
magnons, where the perturbative corrections are less singular at the
thresholds. We then turn our attention to the problem of high-Tc
superconductivity, through the discussion of the stability of the
antiferromagnetic ground state in two spatial dimensions. We argue that this is
caused by an effective mixing of the Goldstone and Higgs modes, which in turn
is caused by an effective Goldstone-boson condensation. The instability of the
antiferromagnetic system is analyzed by studying the non-perturbative behaviour
of the Higgs boson self-energy using the Dyson-Schwinger equations.
