  The formal implications of a quartet coherent state ansatz for proton-neutron
pairing are analyzed. Its nonlinear annihilation operators, which generalize
the BCS linear quasiparticle operators, are computed in the quartetting case.
Their structure is found to generate nontrivial relationships between the many
body correlation functions. The intrinsic structure of the quartet coherent
state is detailed, as it hints to the precise correspondence between the
quartetting picture and the symmetry restored pair condensate picture for the
proton-neutron pairing correlations.
