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2017Sustainable Industrial Processing Summit

Editors:  Kongoli F, Masset P, Rokicki P 
Publisher:  Flogen Star OUTREACH 
Publication Year:  2017 
Pages:  142 pages 
ISBN:  9781987820713 
ISSN:  22911227 (Metals and Materials Processing in a Clean Environment Series) 
An analog of the $S=1/2$ FeynmanDyson propagator is presented in the framework of the $S=1$ Weinberg's 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 FeynmanDyson propagator for the field operator containing the $S=1/2$ self/antiself 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.)