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We consider generalizations of the Radon-Schmid transform on coherent DG/H-Modules, with the intention of obtaining the equivalence between geometric objects (vector bundles) and algebraic objects (D-Modules) characterizing conformal classes in the space-time that determine a space moduli  on coherent sheaves for the securing solutions in field theory . In a major context, elements of derived categories like D-branes and heterotic strings are considered, and using the geometric Langlands program, a moduli space is obtained of equivalence between certain geometrical pictures (non-conformal world sheets ) and physical stacks (derived sheaves), that establishes equivalence between certain theories of super symmetries of field of a Penrose transform that generalizes the implications given by the Langlands program. With it we obtain extensions of a cohomology of integrals for a major class of field equations to corresponding Hecke category.
Considering the finite actions of a field on the matter
and the space which
used to infiltrate their quantum reality at level particle,
methods are developed to serve to base the concept of “intentional action” of a
field and their ordered and supported effects (synergy) that must be realized for the “organized
transformation” of the space and matter. Using path integrals, these transformations
are decoded and their quantum principles are shown.