Gravity, Curvature and Energy: Gravitational Field Intentionality to the Cohesion and Union of the Universe

We use the quantum operators O c G , which are diffeomorphisms of gravity creating the intentionality under the action integrals to prove and determine the gluing intention for adherence of the matter-energy (taking the corresponding mass-energy tensor T ab ) to create complex bodies in the scale of conforming the fragmented Universe such as we know. The reverse is the planting of the energy model of gravity in accordance with the implications in space-time due to the diffeomorphisms of gravity, which were designed to explain the existence of the intention as kernel of the integral operators of the actions with this intention as direction of the energy-matter. The time, in particular, can be shown through instantons of a gauge field (this as electromagnetic field, and in this case appears the torsion) of gravity, which appears in natural way as the same integral operators obtained. Finally, using the complex Riemannian structure of our model of the space-time, and the K-invariant G-structure of the orbits used to obtain curvature, are obtained as consequences of the diffeomorphisms, the field equations to the energy-matter tensor density in each case of the gravitational field

Detection and Measurement of Quantum Gravity by a Curvature Energy Sensor: H-States of Curvature Energy

The curvature energy as spectra of a field observable that is resulted of the variation of energy due to the speed of direction change in the space, is measured and detected by a sensor designed and developed through H-fields of energy that are superposes, obtaining strong variations in the fermion state to the H-torsion (second curvature energy) of the space-time via the gravitational covariant derivative having that the actions can be consigned to these H-fields as Majorana states with a corresponding action of gauge field. Likewise, in this chapter, some geometrical models of these H-states and their spectra of curvature are generated and discussed, which are extrapolated to the design of curvature energy sensors to quantum gravity

The Development and Creation of Intelligent Systems in the next one hundred years

Today the intelligent systems are technological implemented as advanced machines [1] which have high perception, interaction and response to the real world being in much cases an extension of the reality, anticipating events,intertwining remote events, saving life and predicting preferences of human been [2,3] through of robust programming and electronic systems with high performance, optimization and design in operations where are required machines with an strong and complete interacting with the environment [2]; environment which also goes increasing until; in the very near future, to the ends of the Universe

Orbital Integrals on Reductive Lie Groups and Their Algebras

The purpose is to present a complete course on global analysis topics and establish some orbital applications of the integration on topological groups and their algebras to harmonic analysis and induced representations in representation theory

Cycles Cohomology and Geometrical Correspondences of Derived Categories to Field Equations

The integral geometry methods are the techniques could be the more naturally applied to study of the characterization of the moduli stacks and solution classes (represented cohomologically) obtained under the study of the kernels of the differential operators of the corresponding field theory equations to the space-time. Then through a functorial process a classification of differential operators is obtained through of the co-cycles spaces that are generalized Verma modules to the space-time, characterizing the solutions of the field equations. This extension can be given by a global Langlands correspondence between the Hecke sheaves category on an adequate moduli stack and the holomorphic bundles category with a special connection (Deligne connection). Using the classification theorem given by geometrical Langlands correspondences are given various examples on the information that the geometrical invariants and dualities give through moduli problems and Lie groups acting