  We review the role of the spectral condition as a characteristic feature
unifying Minkowski, de Sitter and anti de Sitter Quantum Field Theory. In this
context, we highlight the role of an important class of plane waves which are
either de Sitter or anti de Sitter covariant and are compatible with the
relevant analyticity domains linked to the spectral condition(s). We show again
how to expand the two-point functions and propagators in terms of them and some
of the advantages of doing so rather than using special coordinate systems and
separated variables.
