Integral Geometry and Complex Space-Time Cohomology in Field Theory
Pure and Applied Mathematics Journal
Volume 3, Issue 6-2, December 2014, Pages: 30-37
Received: Dec. 4, 2014; Accepted: Dec. 6, 2014; Published: Dec. 27, 2014
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Authors
Francisco Bulnes, Head of Research Department in Mathematics and Engineering, TESCHA, Chalco, Mexico
Ronin Goborov, Department of Mathematics, Lomonosov University, Moscu, Russia
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Abstract
Through of a cohomological theory based in the relations between integrating invariants and their different differential operators classes in the field equations as well as of functions inside of the integral geometry are established equivalences among cycles and co-cycles of the closed sub-manifolds, line bundles and contours of the space-time modeled as complex Riemannian manifold obtaining a cohomology of general integrals useful in the evaluation and measurement of fields, particles and physical interactions of diverse nature in field theory. Also are used embeddings of cycles in the complex Riemannian manifold through of the dualities: line bundles with cohomological contours and closed sub-manifolds with cohomological functional to build cohomological spaces of integrals as solution classes of the corresponding field equations.
Keywords
Complex Cohomology, Cohomology of Cycles, Cohomological Functional, Integral Operator Cohomology, Integrating Invariants, Integral Topology, Cohomological Classes
To cite this article
Francisco Bulnes, Ronin Goborov, Integral Geometry and Complex Space-Time Cohomology in Field Theory, Pure and Applied Mathematics Journal. Special Issue: Integral Geometry Methods on Derived Categories in the Geometrical Langlands Program. Vol. 3, No. 6-2, 2014, pp. 30-37. doi: 10.11648/j.pamj.s.2014030602.16
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