Hybrid quantization of an inflationary model: The flat case

We present a complete quantization of an approximately homogeneous and isotropic universe with small scalar perturbations. We consider the case in which the matter content is a minimally coupled scalar field and the spatial sections are flat and compact, with the topology of a three-torus. The quantization is carried out along the lines that were put forward by the authors in a previous work for spherical topology. The action of the system is truncated at second order in perturbations. The local gauge freedom is fixed at the classical level, although different gauges are discussed and shown to lead to equivalent conclusions. Moreover, descriptions in terms of gauge-invariant quantities are considered. The reduced system is proven to admit a symplectic structure, and its dynamical evolution is dictated by a Hamiltonian constraint. Then, the background geometry is polymerically quantized, while a Fock representation is adopted for the inhomogeneities. The latter is selected by uniqueness criteria adapted from quantum field theory in curved spacetimes, which determine a specific scaling of the perturbations. In our hybrid quantization, we promote the Hamiltonian constraint to an operator on the kinematical Hilbert space. If the zero mode of the scalar field is interpreted as a relational time, a suitable ansatz for the dependence of the physical states on the polymeric degrees of freedom leads to a quantum wave equation for the evolution of the perturbations. Alternatively, the solutions to the quantum constraint can be characterized by their initial data on the minimum-volume section of each superselection sector. The physical implications of this model will be addressed in a future work, in order to check whether they are compatible with observations.Comment: 20 pages, no figures. v2: minor changes, in particular, abstract shortened, final discussion improve

Effective dynamics of scalar perturbations in a flat Friedmann-Robertson-Walker spacetime in Loop Quantum Cosmology

We study the evolution of a homogeneous and isotropic spacetime whose spatial sections have three-torus topology, coupled to a massless scalar field with small scalar perturbations within loop quantum cosmology. We consider a proposal for the effective dynamics based on a previous hybrid quantization completed by us. Consequently, we introduce a convenient gauge fixing and adopt reduced canonical variables adapted to that hybrid quantum description. Besides, we keep backreaction contributions on the background coming from terms quadratic in the perturbations in the action of the system. We carry out a numerical analysis assuming that the inhomogeneities were in a massless vacuum state at distant past (where the initial data are set). At distant future, we observe a statistical amplification of the modes amplitude in the infrared region, as well as a phase synchronization arising from quantum gravity phenomena. A description of the perturbations in terms of the Mukhanov-Sasaki gauge invariants provides the same qualitative results. Finally, we analyze some consequences of the backreaction in our effective description.Comment: 15 pages, 9 figures. Accepted for publication in Phys. Rev.

A complete hybrid quantization in inhomogeneous cosmology

A complete quantization of a homogeneous and isotropic spacetime with closed spatial sections coupled to a massive scalar field is provided, within the framework of Loop Quantum Cosmology. We identify solutions with their initial data on the minimum volume section, and from this we construct the physical Hilbert space. Moreover, a perturbative study allows us to introduce small inhomogeneities. After gauge fixing, the inhomogeneous part of the system is reduced to a linear field theory. We then adopt a standard Fock representation to quantize these degrees of freedom. For the considered case of compact spatial topology, the requirements of: i) invariance under the spatial isometries, and ii) unitary implementation of the quantum dynamics, pick up a unique Fock representation and a particular set of canonical fields (up to unitary equivalence).Comment: 6 page

La sociedad civil desde la perspectiva metaestructural

The draft of this work lies in raising the definition of civil society from the perspective of the thinker Jacques Bidet. At first highlights the theme of modernity and thus of the existence of a metastructure that resides in a contractual relationship for both sides. At the same type of two types of rationality that run along modernity to give a picture metastructural. Civil society, therefore, from the perspective requires metastructural centricity, the interindividual and associativity. Finally, civil society from this perspective involves a dialectic of conflict that involves a dialectical relationship between the contractual terms of the speech alone can lead to a dialogue of all which is a kind of overdetermination of one ter

Migración de procesos de conversión en Perl a Aspire

Proyecto de Graduación (Bachillerato en Ingeniería en Computación). Instituto Tecnológico de Costa Rica. Escuela de Ingeniería en Computación, 2010.Este proyecto tiene como objetivo analizar una serie de procesos realizados para un cliente de la empresa Search Technologies. Estos procesos transforman documentos electrónicos a un formato más estructurado que permita su posterior indexación y publicación, ya sea tanto en línea como fuera de línea por medio de herramientas como Rocket NXT y Folio. Una vez analizados estos procesos, se han migrado a Aspire, una plataforma para procesamiento de documentos de alto rendimiento perteneciente a Search Technologies. Los procesos escritos en Perl originalmente tienen como entrada documentos en formato Microsoft Word 2003, PDF y HTML. Estos documentos deben ser convertidos a formato HTML si no lo estuvieran y luego recibir una serie de transformaciones textuales mediante el uso de expresiones regulares, con el fin de que su posterior indexación y publicación pueda ser llevada a cabo satisfactoriamente. Este proceso es actualmente semiautomático, es decir, una parte del proceso debe ser realizada manualmente. Este proyecto fue capaz de automatizar el proceso en su totalidad y facilitar futuras implementaciones para otros clientes con necesidades similares. La migración realizada consiste en la creación de pipelines de procesamiento en un ambiente de ejecución concurrente de muchos hilos y el uso extensivo de expresiones regulares. ______________________________________________________________ ABSTRACT The goal of this project is to analyze a series of processes done for a particular client of Search Technologies Company. Those processes transform electronic documents to a more structured format that will allow them to be indexed and published online or offline using Rocket NXT and Folio products. Once analyzed, those processes have been migrated to Aspire, a high performance document processing framework property of Search Technologies. The processes originally written in Perl have as input Microsoft Word 2003 documents, PDF and HTML files. Those documents must be converted to HTML format, if they were not yet, and then passed through a series of text transformations using regular expressions, with the intention of a later successful indexation and publication. This process is semiautomatic, i.e., part of the process is done manually. This project was capable of automate the process entirely and facilitate future implementations for other clients with similar needs. The migration consists of the creation of processing pipelines in a multithread concurrent environment and the extensive use of regular expressions

Alternative method for information georeferencing coordinate system magna-sirgas

El posicionamiento preciso de puntos por sus siglas en ingles PPP, representa un método alternativo y de bajo costo que permite la georreferenciación de mojones o vértices de apoyo, que posteriormente, a partir de ellos, permitirán la captura de información con las precisiones suficientes para las necesidades de los trabajos de consultoría en generalN/AThe precise positioning of points for its acronym in English PPP represents an alternative and inexpensive allowing georeferenced landmarks or vertices of support, then from them, allow the capture of information with sufficient information for needs of consulting work in genera

(Tres problemas clásicos en Análisis Matemático)

Tesis inédita de la Universidad Complutense de Madrid, Facultad de Ciencias Matemáticas, Departamento de Análisis Matemático y Matemática Aplicada, leída el 17-05-2021The title of this dissertation alludes to the study of three classical problems of mathematical analysis. All the results that have been obtained as the fruit of four years of hard work are related, wholly or partially to at least one of the following three fields:• Banach spaces of polynomials: This is a vast field as the educated reader knows well. In particular we have studied continuity properties of polynomials on Banach spaces and topological relationships among polynomial spaces.• Algebraic genericity and lineability: This is the study of the algebraic structure within certain sets in a linear space. We give an answer to a question posed by Gurariy in the early 2000’s and, as a matter of fact, we prove a generalizationto the question formulated by Gurariy. We also link the notion of algebraic genericity to the study of sequences of operators related to Taylor series. • The classical Bohr radius problem: We provide an estimated on the n-dimensional Bohr radius for the polydisk Dn that improves other previous estimates...El título de esta tesis alude al estudio de tres problemas clásicos. Los resultados que se han obtenido, que son el fruto del arduo trabajo llevado a cabo durante los últimos cuatro años, están relacionados, total o parcialmente, con algunos de estos tres temas clásicos del Análisis Matemático: • Espacios de Banach de polinomios: Este es un tema muy extenso, como cualquier lector avezado entenderá enseguida. Siendo más concretos, estudiamos propiedades relacionadas con la continuidad de polinomios en espacios de Banach. También estudiamos la relación existente entre las topologías inducidas por diversas normas en un espacio de polinomios. • Genericidad Algebraica y lineabilidad: Este tema consiste en el estudio de las estructuras algebraicas contenidas en determinados conjuntos de un espacio vectorial o un álgebra. En este sentido, aportamos una solución completa a un problema planteado por V. Gurariy poco después del año 2000. De hecho, la solución proporcionada aquí es, en realidad, una generalización del problema original formulado por V. Gurariy. También investigamos problemas vinculados a la noción de genericidad algebraica en el contexto de sucesiones de operadores relacionados con series de Taylor. • El problema clásico del radio de Bohr: Como principal aportación a este problema, damos una acotación (inferior) del radio de Bohr n-dimensional para el polidisco Dn que mejora estimaciones previas...Fac. de Ciencias MatemáticasTRUEunpu