Theoretical Mathematics & Applications

Extended d− Cohomology and Integral Transforms in Derived Geometry to QFT-equations Solutions using Langlands Correspondences

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  • Abstract

    Through consider several geometrical Langlands correspondences are determined equivalences necessary to the obtaining in the quantized context from differential operators algebra (actions of the algebra on modules) and the holomorphic bundles in the lines bundle stacks required to the model the elements of the different physical stacks, the extension of their field ramifications to the meromorphic case. In this point, is obtained a result that establish a commutative diagram of rings and their spectrum involving the non-commutative Hodge theory, and using integral transforms to establish the decedent isomorphisms in the context of the geometrical stacks to a good Opers, level. The co-cycles obtained through integral transforms are elements of the corresponding deformed category to mentioned different physical stacks. This determines solution classes to the QFT-equations in field theory through the Spectrum of their differential operators.

    Mathematics Subject Classification: 53D37; 11R39; 14D24; 83C60; 11S15
    Keywords: Cycles cohomology; deforming of derived categories; derived categories; field ramifications, generalized Penrose transforms; moduli identities; moduli stacks; quantum field equations; twisted derived categories.