The Epstein-Glaser causal approach to the Light-Front QED4_{4}. I: Free theory

In this work we present the study of light-front field theories in the realm of axiomatic theory. It is known that when one uses the light-cone gauge pathological poles $(k^{+}) ^{-n}$ arises, demanding a prescription to be employed in order to tame these ill-defined poles and to have correct Feynman integrals due to the lack of Wick rotation in such theories. In order to shed a new light on this long standing problem we present here a discussion based on the use rigorous mathematical machinery of distributions combined with physical concepts, such as causality, to show how to deal with these singular propagators in a general fashion without making use of any prescription. The first step of our development will consist in showing how analytic representation for propagators arises by requiring general physical properties in the framework of Wightman's formalism. From that we shall determine the equal-time (anti)commutation relations in the light-front form for the scalar, fermionic fields and for the dynamical components of the electromagnetic field. In conclusion, we introduce the Epstein-Glaser causal method in order to have a mathematical rigorous treatment of the free propagators of the theory, allowing us to discuss the general treatment for propagators of the type $(k^{+}) ^{-n}$. Moreover, we show that at given conditions our results reproduce known prescriptions in the literature.Comment: 34 pages, v2 matching the published versio

Predictors of English Health Literacy among U.S. Hispanic Immigrants: The importance of language, bilingualism and sociolinguistic environment

In the United States, data confirm that Spanish-speaking immigrants are particularly affected by the negative health outcomes associated with low health literacy. Although the literature points to variables such as age, educational background and language, only a few studies have investigated the factors that may influence health literacy in this group. Similarly, the role that bilingualism and/or multilingualism play in health literacy assessment continues to be an issue in need of further research. The purpose of this study was to examine the predictors of English health literacy among adult Hispanic immigrants whose self-reported primary language is Spanish, but who live and function in a bilingual community. It also explored issues related to the language of the instrument. An analysis of data collected through a randomized controlled study was conducted. Results identified English proficiency as the strongest predictor of health literacy (p < 0.001). The results further point to the importance of primary and secondary language in the assessment of heath literacy level. This study raises many questions in need of further investigation to clarify how language proficiency and sociolinguistic environment affect health literacy in language minority adults; proposes language approaches that may be more appropriate for measuring health literacy in these populations; and recommends further place-based research to determine whether the connection between language proficiency and health is generalizable to border communities

Causal approach for the electron-positron scattering in Generalized Quantum Electrodynamics

In this paper we study the generalized electrodynamics contribution for the electron-positron scattering process, $e^{-}e^{+}\rightarrow e^{-}e^{+}$, the Bhabha scattering. Within the framework of the standard model, for energies larger when compared to the electron mass, we calculate the cross section expression for the scattering process. This quantity is usually calculated in the framework of the Maxwell electrodynamics and, by phenomenological reasons, corrected by a cut-off parameter. On the other hand, by considering the generalized electrodynamics instead of Maxwell's, we can show that the effects played by the Podolsky mass is actually a natural cut-off parameter for this scattering process. Furthermore, by means of experimental data of Bhabha scattering we will estimate its lower bound value. Nevertheless, in order to have a mathematically well defined description of our study we shall present our discussion in the framework of the Epstein-Glaser causal theory.Comment: 24 pages, V2 to match published versio

Lesson Study and Service Learning in Teacher Preparation

The aim of this paper is to share an teacher preparation experience that combines Lesson Study (LS) with a Service Learning methodology. This experience is interdisciplinary and includes three subjects from first-grade Childhood Education, carried out at University of Malaga since academic year 2014-2015. Within this framework, our students carry out Service Learning projects for schools in our area that are designed and developed following the LS methodology. Service Learning projects go through the following phases (Puig, J., Martín, & Batlle, 2008): 1) Preparation by the teachers involved in the project; 2) Implementation, i.e. developing the project with the students; 3) Evaluation. The implementation phase also has three sub-phases: preparation, implementation, and round-up. It is here that the LS is developed through the following phases (Soto & Pérez, 2015): 1. Define the problem; 2. Co-operatively design an experimental lesson and its observation process; 3. First experimental lesson; 4. Analyse and review the lesson; 5. Second experimental lesson; 6. Analysis and drafting of conclusions; 7. Presentation in extended context. We were able to gather evidence on how students teachers resolved different cognitive conflicts during the process. We saw how the LS process, with its phases and cooperative work, allows them to combine creativity and unique talents in a common project that acquires meaning and relevance thanks to Service Learning. This provides a framework that facilitates the construction of solid structures related to the meaning of the educational process, and which can be used to recalibrate what it means to be a Childhood School teacher: a creative, relevant, complex experience that requires recreating the knowledge and experience that students bring with them to the University about what it means to be a Childhood School teacher.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech

Aspectos de la recepción del cálculo infinitesimal en Colombia

Se presentará un capítulo de la investigación del trabajo de grado llamado UNA COMPARATIVA HISTORICA EN EL SURGIMIENTO DEL CÁLCULO INFINITESIMAL: ENFOQUES, MOTIVACIONES Y RECEPCION DE LA OBRA DE NEWTON Y LEIBNIZ, en el cual se consideró en una parte de este trabajo un enfoque histórico en Colombia, donde se ven aspectos específicamente en lo relacionado con el cálculo infinitesimal, en cómo fue la llegada de la obra de Newton y Leibniz y la trascendencia que ha tenido la misma en el desarrollo científico-matemático en Colombia. Es así que esta presentación pretende motivar a la comunidad matemática tanto de docentes como de estudiantes a la investigación de la historia de las matemáticas en Colombia