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Integral Geometry Methods on Deformed Categories in Field Theory II
Issue:
Volume 3, Issue 6-2, December 2014
Pages:
1-5
Received:
8 October 2014
Accepted:
11 October 2014
Published:
24 October 2014
Abstract: The integral geometry methods are applied on deformed categories to obtain correspondences in the geometrical Langlands program and construct the due equivalences between geometrical objects of the moduli stacks and algebraic objects of the corresponding categories and their L_(G-opers) characterizing the solution classes to field theory equations in the belonging cohomological context such as H^0 (g[[z] ],V_critical )=C[Op_LG (D^X)] which is natural in the framework of the integral transforms to the generalizing of the Zuckerman functors that will be useful to the obtaining of the different factors of the universal functor of derived sheaves of Harish-Chandra to the Langlands geometrical program in mirror symmetry. The cosmological problem that exists is to reduce the number of field equations that are resoluble under the same gauge field (Verma modules) and to extend the gauge solutions to other fields using the topological groups symmetries that define their interactions. This extension can be given by a global Langlands correspondence between the Hecke sheaves category H_(G^^ ) ∞ on an adequate moduli stack and the holomorphic L_(G-) bundles category with a special connection (Deligne connection). The corresponding 〖D 〗_-modules may be viewed as sheaves of conformal blocks (or co-invariants) (images under a generalized version of the Penrose transform) naturally arising in the framework of conformal field theory.
Abstract: The integral geometry methods are applied on deformed categories to obtain correspondences in the geometrical Langlands program and construct the due equivalences between geometrical objects of the moduli stacks and algebraic objects of the corresponding categories and their L_(G-opers) characterizing the solution classes to field theory equations ...
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Coverings and Axions: Topological Characterizing of the Energy Coverings in Space-Time
Mario Ramírez,
Luis Ramírez,
Oscar Ramírez,
Francisco Bulnes
Issue:
Volume 3, Issue 6-2, December 2014
Pages:
6-11
Received:
8 October 2014
Accepted:
11 October 2014
Published:
24 October 2014
Abstract: Inside the QFT and TFT frame is developed a geometrical and topological model of one wrapping energy particle or “axion” to establish the diffeomorphic relation between space and time through of universal coverings. Then is established a scheme that relates both aspects, time and space through of the different objects that these include and their spectrum that is characterized by their wrapping energy.
Abstract: Inside the QFT and TFT frame is developed a geometrical and topological model of one wrapping energy particle or “axion” to establish the diffeomorphic relation between space and time through of universal coverings. Then is established a scheme that relates both aspects, time and space through of the different objects that these include and their s...
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Moduli Spaces, Non-Commutative Geometry and Deformed Differential Categories
Issue:
Volume 3, Issue 6-2, December 2014
Pages:
12-19
Received:
25 October 2014
Accepted:
2 November 2014
Published:
5 November 2014
Abstract: The following research plays a central role in deformation theory. If x, is a moduli space over a field k, of characteristic zero, then a formal neighborhood of any point xϵx, is controlled by a differential graded Lie algebra. Then using the derived categories language we give an analogous of the before sentence in the setting of non-commutative geometry, considering some aspects E∞— rings and derived moduli problems related with these rings. After is obtained a scheme to spectrum; by functor Spec and their ∞— category functor inside of the space Fun_(hoat_∞ )to these E∞— rings and their derived moduli in field theory.
Abstract: The following research plays a central role in deformation theory. If x, is a moduli space over a field k, of characteristic zero, then a formal neighborhood of any point xϵx, is controlled by a differential graded Lie algebra. Then using the derived categories language we give an analogous of the before sentence in the setting of non-commutative g...
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Functors on ∞- Categories and the Yoneda Embedding
Issue:
Volume 3, Issue 6-2, December 2014
Pages:
20-25
Received:
12 November 2014
Accepted:
18 November 2014
Published:
24 November 2014
Abstract: Through the application of the Yoneda embedding in the context of the ∞- categories is obtained a classification of functors with their corresponding extended functors in the geometrical Langlands program. Also is obtained a functor formula that can be considered in the extending of functors to obtaining of generalized Verma modules. In this isomorphism formula are considered the Verma modules as classifying spaces of these functors.
Abstract: Through the application of the Yoneda embedding in the context of the ∞- categories is obtained a classification of functors with their corresponding extended functors in the geometrical Langlands program. Also is obtained a functor formula that can be considered in the extending of functors to obtaining of generalized Verma modules. In this isomor...
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The Recillas’s Conjecture on Szegö Kernels Associated to Harish-Chandra Modules
Francisco Bulnes,
Kubo Watanabe,
Ronin Goborov
Issue:
Volume 3, Issue 6-2, December 2014
Pages:
26-29
Received:
22 November 2014
Accepted:
27 November 2014
Published:
29 November 2014
Abstract: The solution of the field equations that involves non-flat differential operators (curved case) can be obtained as the extensions Φ+Szegö operators in G/K with G, a non-compact Lie group with K, compact. This could be equivalent in the context of the Harish-Chandra modules category to the obtaining of extensions in certain sense (Cousin complexes of sheaves of differential operators to their classification) of Verma modules as classifying spaces of these differential operators and their corresponding integrals through of geometrical integral transforms.
Abstract: The solution of the field equations that involves non-flat differential operators (curved case) can be obtained as the extensions Φ+Szegö operators in G/K with G, a non-compact Lie group with K, compact. This could be equivalent in the context of the Harish-Chandra modules category to the obtaining of extensions in certain sense (Cousin complexes o...
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Integral Geometry and Complex Space-Time Cohomology in Field Theory
Francisco Bulnes,
Ronin Goborov
Issue:
Volume 3, Issue 6-2, December 2014
Pages:
30-37
Received:
4 December 2014
Accepted:
6 December 2014
Published:
27 December 2014
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.
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 mod...
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Approaching by DX- Schemes and Jets to Conformal Blocks in Commutative Moduli Schemes
Issue:
Volume 3, Issue 6-2, December 2014
Pages:
38-43
Received:
3 December 2014
Accepted:
8 December 2014
Published:
10 January 2015
Abstract: The DX-schemes (and their particular tools example jets) are related to determine conformal blocks of space-time pieces that are invariant under conformal transformations. All algebras will be commutative and Sym will always denote SymOX However, all Hom, and , will be understood over the base field k. This will permit the construction of one formal moduli problem on the base of CAlgk whose objects are obtained as limits of the corresponding jets in an AffSpec. An algebra B, belonging to the DX-schemes to the required formal moduli problem is the image under a corresponding generalized Penrose transform, in the conformal context, of many pieces of the space-time, having a structure as objects in commutative rings of CAlgk each one.
Abstract: The DX-schemes (and their particular tools example jets) are related to determine conformal blocks of space-time pieces that are invariant under conformal transformations. All algebras will be commutative and Sym will always denote SymOX However, all Hom, and , will be understood over the base field k. This will permit the construction of one forma...
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