Statistical field theories deformed within different calculi

TL;DR

This paper develops generalized field-theoretical frameworks for statistically distributed fields within various deformed calculi, connecting generating functionals with correlators and Green functions, and extending to systems with symmetries and constraints.

Contribution

It introduces a unified approach to field theories in different deformed calculi, linking generating functionals with correlators and Green functions, and generalizing schemes in Naudts' spirit.

Findings

Constructed generating functionals for deformed calculi

Connected correlators with generating functionals

Derived formal equations for symmetric constrained systems

Abstract

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.