Symmetry Conserving Dynamical Mappings

Using the concept of dynamical mappings, two symmetry conserving nonperturbative approaches are presented. The first is based on the 1/N-expansion and sorted out using Holstein-Primakoff mapping. The second consists of dynamically mapping the canonical fields into the corresponding currents. It is argued, either by comparing the Fock spaces or the observables, that the latter constitutes a higher approach which transcends the 1/N-expansion and contains the dynamics generated by the Gaussian functional approach.