Statistical field theories deformed within different calculi

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.

12 pages, 3 figures

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Cited by in corpus (5)

• Theoretical foundations and mathematical formalism of the power-law tailed statistical distributions
• Entropic Forms and Related Algebras
• Physical origin of the power-law tailed statistical distributions
• Relativistic Roots of $\kappa$-Entropy
• Power-Law tailed statistical distributions and Lorentz transformations