Geometrical Langlands Ramifications and Differential Operators Classification by Coherent D-Modules in Field Theory  

作　　者：Francisco Bulnes 

机构地区：[1]Department of Research in Mathematics and Engineering, TESCHA, Federal Highway Mexico-Cuautla Tlapala "La Candelaria"Chalco. State of Mexico, P. C. 56641, Mexico.

出　　处：《Journal of Mathematics and System Science》2013年第10期491-507,共17页数学和系统科学（英文版）

摘　　要：Spaces of equivalence modulo a relation of congruence are constructed on field solutions to establish a theory of the universe that includes the theory QFT （Quantum Field theory）, the SUSY （Super-symmetry theory） and HST （heterotic string theory） using the sheaves correspondence of differential operators of the field equations and sheaves of coherent D - Modules [1]. The above mentioned correspondence use a Zuckerman functor that is a factor of the universal functor of derived sheaves of Harish-Chandra to the Langlands geometrical program in mirror symmetry [2, 3]. The obtained development includes complexes of D - modules of infinite dimension, generalizing for this way, the BRST-cohomology in this context. With it, the class of the integrable systems is extended in mathematical physics and the possibility of obtaining a general theory of integral transforms for the space - time （integral operator cohomology [4]）, and with it the measurement of many of their observables [5]. Also tends a bridge to complete a classification of the differential operators for the different field equations using on the base of Verma modules that are classification spaces of SO（l, n ＋ 1）, where elements of the Lie algebra al（1, n ＋ 1）, are differential operators, of the equations in mathematical physics [1]. 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 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 version of the Penrose transform [1, 6]） naturally arising in the framework of conformal field theory.

关 键 词：Langlands correspondence Hecke sheaves category moduli stacks Verma modules generalized D-modules Vermamodule extensions 

分 类 号：O175.3[理学—数学] O413.3[理学—基础数学]