  We discuss the necessity of using non-standard boson operators for
diagonalizing quadratic bosonic forms which are not positive definite and its
convenience for describing the temporal evolution of the system. Such operators
correspond to non-hermitian coordinates and momenta and are associated with
complex frequencies. As application, we examine a bosonic version of a BCS-like
pairing Hamiltonian, which, in contrast with the fermionic case, is stable just
for limited values of the gap parameter and requires the use of the present
extended treatment for a general diagonal representation. The dynamical
stability of such forms and the occurrence of non-diagonalizable cases are also
discussed.
