A uniqueness criterion for the Fock quantization of scalar fields with time dependent mass

A major problem in the quantization of fields in curved spacetimes is the ambiguity in the choice of a Fock representation for the canonical commutation relations. There exists an infinite number of choices leading to different physical predictions. In stationary scenarios, a common strategy is to select a vacuum (or a family of unitarily equivalent vacua) by requiring invariance under the spacetime symmetries. When stationarity is lost, a natural generalization consists in replacing time invariance by unitarity in the evolution. We prove that, when the spatial sections are compact, the criterion of a unitary dynamics, together with the invariance under the spatial isometries, suffices to select a unique family of Fock quantizations for a scalar field with time dependent mass.Comment: 11 pages, version accepted for publication in Classical and Quantum Gravit

Criteria for the determination of time dependent scalings in the Fock quantization of scalar fields with a time dependent mass in ultrastatic spacetimes

For Klein-Gordon fields, it is well known that there exist an infinite number of nonequivalent Fock representations of the canonical commutation relations and, therefore, of inequivalent quantum theories. A context in which this kind of ambiguities arises and prevents the derivation of robust results is, e.g., in the quantum analysis of cosmological perturbations. In these situations, typically, a suitable scaling of the field by a time dependent function leads to a description in an auxiliary static background, though the nonstationarity still shows up in a time dependent mass. For such a field description, and assuming the compactness of the spatial sections, we recently proved in three or less spatial dimensions that the criteria of a natural implementation of the spatial symmetries and of a unitary time evolution are able to select a unique class of unitarily equivalent vacua, and hence of Fock representations. In this work, we succeed to extend our uniqueness result to the consideration of all possible field descriptions that can be reached by a time dependent canonical transformation which, in particular, involves a scaling of the field by a function of time. This kind of canonical transformations modify the dynamics of the system and introduce a further ambiguity in its quantum description, exceeding the choice of a Fock representation. Remarkably, for any compact spatial manifold in less than four dimensions, we show that our criteria eliminate any possible nontrivial scaling of the field other than that leading to the description in an auxiliary static background. Besides, we show that either no time dependent redefinition of the field momentum is allowed or, if this may happen, the redefinition does not introduce any Fock representation that cannot be obtained by a unitary transformation.Comment: 37 pages. Modified title. Improved discussion concerning the spatial symmetry group. New section (section VI

Pabellón-puente. Expo 2008. Concepción estructural y proyecto

El Pabellón-Puente para la Expo2008 de Zaragoza es un edificio tendido sobre el río Ebro que sirve como puerta de entrada al recinto de la Expo 2008 a la vez que alberga en su interior espacios expositivos dispuestos en varios niveles. Es un proyecto en el que la estructura es protagonista esencial por su complejidad y porque está fuertemente integrada en el concepto arquitectónico. Fue objeto de un concurso internacional de arquitectura en el que el proyecto ganador resultó ser el propuesto por el equipo de la arquitecta Zaha Hadid. Se trata de una estructura metálica de 250 m de longitud, planteada con dos vanos de 100 y 150 m de luz respectivamente, con geometría curva en planta y sección transversal variable en anchura, altura y geometría. El proyecto de construcción lo realizó FHECOR Ingenieros Consultores y la construcción fue llevada a cabo por la UTE formada por DRAGADOS y URSSA

Uniqueness of the Fock quantization of scalar fields in a Bianchi I cosmology with unitary dynamics

The Fock quantization of free scalar fields is subject to an infinite ambiguity when it comes to choosing a set of annihilation and creation operators, choice that is equivalent to the determination of a vacuum state. In highly symmetric situations, this ambiguity can be removed by asking vacuum invariance under the symmetries of the system. Similarly, in stationary backgrounds, one can demand time-translation invariance plus positivity of the energy. However, in more general situations, additional criteria are needed. For the case of free (test) fields minimally coupled to a homogeneous and isotropic cosmology, it has been proven that the ambiguity is resolved by introducing the criterion of unitary implementability of the quantum dynamics, as an endomorphism in Fock space. This condition determines a specific separation of the time dependence of the field, so that this splits into a very precise background dependence and a genuine quantum evolution. Furthermore, together with the condition of vacuum invariance under the spatial Killing symmetries, unitarity of the dynamics selects a unique Fock representation for the canonical commutation relations, up to unitary equivalence. In this work, we generalize these results to anisotropic spacetimes with shear, which are therefore not conformally symmetric, by considering the case of a free scalar field in a Bianchi I cosmology.Comment: 23 pages. Updated to match published versio

Arquitectura de barro. Reconstrucción gráfica del hábitat del inicio de la Edad del Bronce en el interior peninsular

[ES] La excavación de dos yacimientos de la Edad del Bronce en la provincia de Soria aporta datos sobre la estructura y urbanismo de los poblados en altura entre el II y III milenio AC, los primeros conocidos en la zona del Alto Duero.Los materiales constructivos encontrados informan sobre las soluciones arquitectónicas utilizadas. Su distribución y la de los ajuares domésticos permiten interpretar la organización de los poblados y la especialización de actividades en relación con los espacios de habitación.De tal forma, se cuenta con una completa información para reconstruir virtualmente estos poblados, ajustándose a las evidencias arqueológicas e integrándolos en un modelo digital del terreno.[EN] The results of the excavation of two archaeological sites from the Bronze Age in the province of Soria bring forward valuable information on the structure and town planning of the villages set up on high grounds in the second and third millennium BC, which are the oldest villages known in the upper area Duero river.The building materials found on the sites tell us on the architectural solutions used in those villages. Their distribution, as well as the outlay of the household objects allow for an interpretation of the organization of the villages and the specialization of activities in relation to the different rooms.In this way, one is provided with relevant information for a virtual reconstruction of these villages, complying with archaeological findings and integrating them into a digital model of the area.Fernández Moreno, JJ.; Almeida Olmedo, JR. (2011). Arquitectura de barro. Reconstrucción gráfica del hábitat del inicio de la Edad del Bronce en el interior peninsular. Virtual Archaeology Review. 2(3):93-97. https://doi.org/10.4995/var.2011.4620OJS939723BELLIDO BLANCO, A, (1996): Los campos de hoyos. Inicio de la economía agrícola en la submeseta norte. Studia Archeologica, 85. Universidad de Valladolid.DÍAZ DEL RÍO ESPAÑOL, P. (2001): La formación del Paisaje Agrario: Madrid en el III y II milenios BC. Arqueología, Paleontología y Etnografía, Consejería de las Artes. Comunidad de Madrid, Madrid.GRAU MIRA, I. (Ed) (2006): La aplicación de los SIG en la arqueología del paisaje. Universidad de Alicante.HARRISON, R. J.; MORENO LÓPEZ, G. Y A. J. LEGGE (1994): Moncín: un poblado de la Edad del Bronce (Borja, Zaragoza), Colección Arqueología, 16, Diputación General de Aragón, Departamento de Educación y Cultura, Zaragoza.JIMENO, A. Y J. J. FERNÁNDEZ MORENO (1991): Los Tolmos de Caracena (Soria) Campañas de 1981 y 1982). Aportación al Bronce Medio de la Meseta. Excavaciones Arqueológicas en España, 161. Ministerio de Cultura, Madrid. (1992): El poblamiento desde el Neolítico a la Edad del Bronce constantes y cambios; 2º Symposium de Arqueología Soriana (octubre, 1989), Vol. I Col. Temas Sorianos, núm. 20; Diputación Provincial de Soria: 71-101.JIMENO, A.; FERNÁNDEZ MORENO, J. J. Y Mª L. REVILLA (1988): Asentamientos de la Edad del Bronce en la provincia de Soria: Consideraciones sobre los contextos culturales del Bronce Antiguo; Noticiario Arqueológico Hispanico, 30: 83-119.JIMENO, A.; MARTÍNEZ NARANJO, J. P; CHAÍN, A, Y H. ALGARRA (2007): Incendio en Numancia, una experimentación no pensada. Arqueología experimental en la Península Ibérica: investigación, didáctica y patrimonio / coord. Ramos Sáinz, M L.; González Urquijo, J. E., y J. Baena Preysler: 245- 253MALDONADO RAMOS, L. Y F. VELA COSSÍO (1988): De arquitectura y Arqueología, Ed. Munilla-Lería, 10, Madrid.RODRÍGUEZ MARCOS, J. A. Y A. L. PALOMINO LÁZARO (1997): Un asentamiento castreño del Bronce Antiguo en la cuenca del Duero: El Pico Romero en Santa Cruz de la Salceda (Burgos). II Congreso de Arqueología Peninsular, Zamora, del 24 al 27 de septiembre de 1996, Fundación Rei Afonso Henriques, Tomo II Neolítico, Calcolítico y Bronce: 579-590.SANZ ARAGONÉS, A., J.P. BENITO BATANERO Y C. TABERNERO GALÁN (2006) : Construcciones con cubierta vegetal en el sur de la provincia de Soria. Junta de Castilla y León.SIGAUT, F. (1979): La redécouverte des silos a grains en Europe Occidentale, 1708-1880, en Gast, M y F. Sigaut (Edits.): Les techniques de conservation des grains à long terme. Leur rôle dans la dynamique des systèmes de cultures et de sociétés, Centre National de la Recherche Scientifique, Paris: 15-3

A unique Fock quantization for fields in non-stationary spacetimes

In curved spacetimes, the lack of criteria for the construction of a unique quantization is a fundamental problem undermining the significance of the predictions of quantum field theory. Inequivalent quantizations lead to different physics. Recently, however, some uniqueness results have been obtained for fields in non-stationary settings. In particular, for vacua that are invariant under the background symmetries, a unitary implementation of the classical evolution suffices to pick up a unique Fock quantization in the case of Klein-Gordon fields with time-dependent mass, propagating in a static spacetime whose spatial sections are three-spheres. In fact, the field equation can be reinterpreted as describing the propagation in a Friedmann-Robertson-Walker spacetime after a suitable scaling of the field by a function of time. For this class of fields, we prove here an even stronger result about the Fock quantization: the uniqueness persists when one allows for linear time-dependent transformations of the field in order to account for a scaling by background functions. In total, paying attention to the dynamics, there exists a preferred choice of quantum field, and only one $SO(4)$-invariant Fock representation for it that respects the standard probabilistic interpretation along the evolution. The result has relevant implications e.g. in cosmology.Comment: Typos correcte

Modelos culturales en un contexto multicultural

Este artículo parte de una investigación más amplia que analiza las diferencias que existen entre los modelos familiares en el contexto intercultural de la Ciudad Autónoma de Ceuta. Para ello, tenemos en cuenta como la cultura puede modelar hábitos y las expectativas en el núcleo familiar. El estudio se ha realizado sobre una muestra de 335 padres y madres de alumnos/as de 5 años, del tercer curso de Educación Infantil, a los que se aplicó un cuestionario sobre modelos culturales relacionados con aspectos que pudieran representar a las dos culturas con mayor presencia en este ámbito. Se utilizaron variables que definen componentes relacionados con costumbres, hábitos, lenguaje, valores, normas, expectativas y convivencia. En el instrumento elaborado se definen los diferentes modelos culturales, fundamentados en un marco teórico en el que se reconocen las dimensiones básicas en las que se sustentan estas diferencias culturales, así como el grado de identidad cultural de las familias en contextos multiculturales. Los resultados constatan diferencias culturales que nos permiten establecer dos modelos que presentan una estructura familiar diferente para ambas culturas, una situación que puede modelar la educación de los niños/as antes de iniciar la Educación Infantil

CDIO Experiences in Biomedical Engineering: Preparing Spanish Students for the Future of Medicine and Medical Device Technology

Biomedical engineering is one of the more recent fields of engineering, aimed at the application of engineering principles, methods and design concepts to medicine and biology for healthcare purposes, mainly as a support for preventive, diagnostic or therapeutic tasks. Biomedical engineering professionals are expected to achieve, during their studies and professional practice, considerable knowledge of both health sciences and engineering. Studying biomedical engineering programmes, or combining pre-graduate studies in life sciences with graduate studies in engineering, or vice versa, are typical options for becoming qualified biomedical engineering professionals, although there are additional interesting alternatives, to be discussed. According to our experience, the graduates and post-graduates from multidisciplinary engineering programmes, not just from biomedical engineering, but also from more traditional fields including industrial, mechanical and telecommunications engineering, can play varied and very relevant roles in the biomedical industry and in extremely complex biomedical device development projects. In spite of the different ways of becoming a professional of the biomedical engineering field, it is true that their impact as successful professionals can be importantly increased, by means of an adequate integration into their curricula of fundamental biomedical engineering design concepts, methodologies and good practices, applied to the development of biomedical devices. In this study we present the complete development and comparative study of three courses, belonging to different plans of study taught at the Technical University of Madrid and benefiting from using a CDIO approach focused on the development of biomedical devices. The three courses are “Development of Medical Devices”, “Bioengineering Design” and “Biomedical Engineering”, respectively belonging to the “Bachelor’s Degree in Biomedical Engineering”, to the “Master’s Degree in Industrial Engineering” and to the “Master’s Degree in Mechanical Engineering”. During the courses, groups of students live through the development process of different biomedical devices aimed at providing answers to relevant social needs. Depending on their background and European credits assigned to the different courses, students carry out more conceptual projects or are able to live through more complete CDIO experiences. Main benefits, lessons learned and future challenges, linked to these courses, are analyzed, taking account of the results from 2014-2015 academic year

Experimental Feeding and Growth of Turbot (Scophthalmus maximus L.) from 0.5 To 2.7 Kg in Galicia (NW Spain)

Two groups of turbot, Scophthalmus maximus L., of 0.5 and 1.2 kg initial mean weight were fed a semimoist diet containing fish, fish meal and vitamin-mineral complex. The trial was carried out in tanks of 16 cubic meters, for aperiod of a year. Resul ts on feed conversion index and growth in weight are give

Uniqueness of the Fock quantization of fields with unitary dynamics in nonstationary spacetimes

The Fock quantization of fields propagating in cosmological spacetimes is not uniquely determined because of several reasons. Apart from the ambiguity in the choice of the quantum representation of the canonical commutation relations, there also exists certain freedom in the choice of field: one can scale it arbitrarily absorbing background functions, which are spatially homogeneous but depend on time. Each nontrivial scaling turns out into a different dynamics and, in general, into an inequivalent quantum field theory. In this work we analyze this freedom at the quantum level for a scalar field in a nonstationary, homogeneous spacetime whose spatial sections have $S^3$ topology. A scaling of the configuration variable is introduced as part of a linear, time dependent canonical transformation in phase space. In this context, we prove in full detail a uniqueness result about the Fock quantization requiring that the dynamics be unitary and the spatial symmetries of the field equations have a natural unitary implementation. The main conclusion is that, with those requirements, only one particular canonical transformation is allowed, and thus only one choice of field-momentum pair (up to irrelevant constant scalings). This complements another previous uniqueness result for scalar fields with a time varying mass on $S^3$, which selects a specific equivalence class of Fock representations of the canonical commutation relations under the conditions of a unitary evolution and the invariance of the vacuum under the background symmetries. In total, the combination of these two different statements of uniqueness picks up a unique Fock quantization for the system. We also extend our proof of uniqueness to other compact topologies and spacetime dimensions.Comment: 12 page