The 2-dimensional O(4) symmetric Heisenberg ferromagnet in terms of rotation-invariant variables

After the introduction of rotation-invariant auxiliary variables, the integration over all rotation-variant variables (spins) in the O(4) symmetric two-dimensional Heisenberg ferromagnet can be performed. The resulting new hamiltonian involves a sum over closed loops. It is complex and invariant under U(1) gauge transformations. Rühl's boson representation is used to derive the result.