  Within framework of basic-deformed and finite-difference calculi, as well as
deformation procedures proposed by Tsallis, Abe, and Kaniadakis to be
generalized by Naudts, we develop field-theoretical schemes of statistically
distributed fields. We construct a set of generating functionals and find their
connection with corresponding correlators for basic-deformed,
finite-difference, and Kaniadakis calculi. Moreover, we introduce pair of
additive functionals, whose expansions into deformed series yield both Green
functions and their irreducible proper vertices. We find as well formal
equations, governing by the generating functionals of systems which possess a
symmetry with respect to a field variation and are subjected to an arbitrary
constrain. Finally, we generalize field-theoretical schemes inherent in
concrete calculi in the Naudts spirit.
