  An analog of the S=1/2 Feynman-Dyson propagator is presented in the framework
of the S=1 Weinberg theory. The basis for this construction is the concept of
the Weinberg field as a system of four field functions differing by parity and
by dual transformations. Next, we analyze the recent controversy in the
definitions of the Feynman-Dyson propagator for the field operator containing
the S=1/2 self/anti-self charge conjugate states in the papers by D. Ahluwalia
et al. and by W. Rodrigues Jr. et al. The solution of this mathematical
controversy is obvious. It is related to the necessary doubling of the Fock
Space (as in the Barut and Ziino works), thus extending the corresponding
Clifford Algebra. However, the logical interrelations of different mathematical
foundations with the physical interpretations are not so obvious. Physics
should choose only one correct formalism, it is not clear, why two correct
mathematical formalisms (which are based on the same postulates) lead to
different physical results?
