Rotor spectra, berry phases, and monopole fields: From antiferromagnets to QCD

The order parameter of a finite system with a spontaneously broken continuous global symmetry acts as a quantum mechanical rotor. Both antiferromagnets with a spontaneously broken SU(2)(s) spin symmetry and massless QCD with a broken SU(2)(L)xSU(2)(R) chiral symmetry have rotor spectra when considered in a finite volume. When an electron or hole is doped into an antiferromagnet or when a nucleon is propagating through the QCD vacuum, a Berry phase arises from a monopole field and the angular momentum of the rotor is quantized in half-integer units.