Hybrid Quantum Cosmology: Combining Loop and Fock Quantizations

As a necessary step towards the extraction of realistic results from Loop Quantum Cosmology, we analyze the physical consequences of including inhomogeneities. We consider in detail the quantization of a gravitational model in vacuo which possesses local degrees of freedom, namely, the linearly polarized Gowdy cosmologies with the spatial topology of a three-torus. We carry out a hybrid quantization which combines loop and Fock techniques. We discuss the main aspects and results of this hybrid quantization, which include the resolution of the cosmological singularity, the polymeric quantization of the internal time, a rigorous definition of the quantum constraints and the construction of their solutions, the Hilbert structure of the physical states, and the recovery of a conventional Fock quantization for the inhomogeneities.Comment: 24 pages, published in International Journal of Modern Physics A, Special Issue: Proceedings of the Second Workshop on Quantum Gravity and Noncommutative Geometry (Lisbon, Portugal

Further Improvements in the Understanding of Isotropic Loop Quantum Cosmology

The flat, homogeneous, and isotropic universe with a massless scalar field is a paradigmatic model in Loop Quantum Cosmology. In spite of the prominent role that the model has played in the development of this branch of physics, there still remain some aspects of its quantization which deserve a more detailed discussion. These aspects include the kinematical resolution of the cosmological singularity, the precise relation between the solutions of the densitized and non-densitized versions of the quantum Hamiltonian constraint, the possibility of identifying superselection sectors which are as simple as possible, and a clear comprehension of the Wheeler-DeWitt (WDW) limit associated with the theory in those sectors. We propose an alternative operator to represent the Hamiltonian constraint which is specially suitable to deal with these issues in a satisfactory way. In particular, with our constraint operator, the singularity decouples in the kinematical Hilbert space and can be removed already at this level. Thanks to this fact, we can densitize the quantum Hamiltonian constraint in a rigorous manner. Besides, together with the physical observables, this constraint superselects simple sectors for the universe volume, with a support contained in a single semiaxis of the real line and for which the basic functions that encode the information about the geometry possess optimal physical properties. Namely, they provide a no-boundary description around the cosmological singularity and admit a well-defined WDW limit in terms of standing waves. Both properties explain the presence of a generic quantum bounce replacing the singularity at a fundamental level, in contrast with previous studies where the bounce was proved in concrete regimes and focusing on states with a marked semiclassical behavior.Comment: 13 pages, version accepted for publication in Physical Review

Unitary evolution and uniqueness of the Fock representation of Dirac fields in cosmological spacetimes

We present a privileged Fock quantization of a massive Dirac field in a closed Friedmann-Robertson-Walker cosmology, partially selected by the criteria of invariance of the vacuum under the symmetries of the field equations, and unitary implementation of the dynamics. When quantizing free scalar fields in homogeneous and isotropic spacetimes with compact spatial sections, these criteria have been shown to pick out a unique Fock representation (up to unitary equivalence). Here, we employ the same criteria for fermion fields and explore whether that uniqueness result can be extended to the case of the Fock quantization of fermions. For the massive Dirac field, we start by introducing a specific choice of the complex structure that determines the Fock representation. Such structure is invariant under the symmetries of the equations of motion. We then prove that the corresponding representation of the canonical anticommutation relations admits a unitary implementation of the dynamics. Moreover, we construct a rather general class of representations that satisfy the above criteria, and we demonstrate that they are all unitarily equivalent to our previous choice. The complex structures in this class are restricted only by certain conditions on their asymptotic behavior for modes in the ultraviolet sector of the Dirac operator. We finally show that, if one assumes that these asymptotic conditions are in fact trivial once our criteria are fulfilled, then the time-dependent scaling in the definition of the fermionic annihilation and creation-like variables is essentially unique.Comment: 24 page

El acuerdo para la mejora del crecimiento y el empleo en la perspectiva económica

El análisis económico del último gran pacto social en materia de mercado de trabajo, observado desde la perspectiva su incardinación en el contexto de otros acuerdos y reformas precedentes, así como de las reformas que aún pueden considerarse pendientes, es el objetivo principal de este trabajo. En ese sentido, quizás el primer dato a destacar es el del papel de la concertación social, en términos de estabilidad política y social, en cuanto que torna en elemento preciso para afianzar una dinámica de crecimiento continuado de la formación bruta de capital, vía atracción de inversiones externas o vía estimulo al ahorro interno. Desde un punto de vista objetivo o material, la temporalidad —la lucha contra el exceso peso de la misma—, que ha sido la transformación más importante en las relaciones laborales en los últimos 20 años del siglo pasado y que caracterizó la evolución del mercado de trabajo español, se constituye en el eje vertebrador de la reforma, más que la propia creación de empleo. Pero también cabe resaltar, pese a que no se trata de una reforma integral, que cabe esperar que efectos del nuevo marco regulatorio se extiendan a su vez sobre la dinámica de la productividad, en la medida en que el encarecimiento relativo en el uso del trabajo temporal lleve a una búsqueda de recortes de los cotes laborales a través de mejoras en el rendimiento del trabajo. De obtenerse tales resultados, cabría hablar de un éxito importante en la aplicación del acuerdo. Como punto de conclusión se ha de señalar en todo caso que todavía es pronto para poder hacer valoraciones sobre las consecuencias que la puesta en marcha del acuerdo para la mejora del crecimiento y el empleo. Hacer previsiones sobre su evolución futura es deslizarse por un terreno resbaladizo. El fuerte crecimiento del empleo que se ha puesto de manifiesto en la última década ha estado enmarcado en un entorno general de estabilidad económica de reducción de inflación y de tipos de interés en relación a la puesta en marcha del euro como moneda única. Las circunstancias del entorno ha cambiado en los últimos años y el fenómeno más relevante que se está produciendo en la economía y sociedad española de la última década es el creciente fenómeno inmigratorio. Los efectos de la incorporación de estos trabajadores a las nuevas condiciones del mercado laboral repercutirán en los resultados del acuerdo que aquí hemos recogido

Uniqueness of the Fock quantization of Dirac fields in 2+1 dimensions

We study the Fock quantization of a free Dirac field in 2+1-dimensional backgrounds which are conformally ultrastatic, with a time-dependent conformal factor. As it is typical for field theories, there is an infinite ambiguity in the Fock representation of the canonical anticommutation relations. Different choices may lead to unitarily inequivalent theories that describe different physics. To remove this ambiguity one usually requires that the vacuum be invariant under the unitary transformations that implement the symmetries of the equations of motion. However, in non-stationary backgrounds, where time translation is not a symmetry transformation, the requirement of vacuum invariance is in general not enough to fix completely the Fock representation. We show that this problem is overcome in the considered scenario by demanding, in addition, a unitarily implementable quantum dynamics. The combined imposition of these conditions selects a unique family of equivalent Fock representations. Moreover, one also obtains an essentially unique splitting of the time variation of the Dirac field into an explicit dependence on the background scale factor and a quantum evolution of the corresponding creation and annihilation operators.Comment: 24 pages. Document replaced to match published versio

Inhomogeneous Loop Quantum Cosmology: Hybrid Quantization of the Gowdy Model

The Gowdy cosmologies provide a suitable arena to further develop Loop Quantum Cosmology, allowing the presence of inhomogeneities. For the particular case of Gowdy spacetimes with the spatial topology of a three-torus and a content of linearly polarized gravitational waves, we detail a hybrid quantum theory in which we combine a loop quantization of the degrees of freedom that parametrize the subfamily of homogeneous solutions, which represent Bianchi I spacetimes, and a Fock quantization of the inhomogeneities. Two different theories are constructed and compared, corresponding to two different schemes for the quantization of the Bianchi I model within the {\sl improved dynamics} formalism of Loop Quantum Cosmology. One of these schemes has been recently put forward by Ashtekar and Wilson-Ewing. We address several issues including the quantum resolution of the cosmological singularity, the structure of the superselection sectors in the quantum system, or the construction of the Hilbert space of physical states.Comment: 16 pages, version accepted for publication in Physical Review

Desaceleración económica y crisis. El mercado de trabajo en el primer trimestre de 2008

En el primer trimestre de 2008 la economía española parece haber entrado ya claramente en una nueva fase del ciclo económico. Las previsiones de crecimiento económico se han reducido drásticamente respecto a las de trimestres anteriores. La desaceleración económica se traduce en el comportamiento de las principales variables laborales. El desempleo crece en España y en Andalucía y el crecimiento de la ocupación se ha detenido. La crisis es especialmente grave en el caso del sector de la construcción. La tasa de paro en Andalucía ha alcanzado el 14,83%.Las perspectivas para los próximos trimestres no son muy optimistas

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

Cryopreservation of embryogenic cell suspensions of the Spanish grapevine cultivars ‘Albariño’ and ‘Tempranillo’

Embryogenic cell suspensions of two elite Spanish grapevine cultivars (‘Albariño’ and ‘Tempranillo’) were successfully cryopreserved by encapsulation-dehydration. The method implied the encapsulation of cells in alginate beads, subsequent culture in liquid medium with 1 M sucrose for 4 days, and desiccation for 2-4 h in the flow of a laminar-flow bench, before immersing in liquid nitrogen. With this simple method, up to 50 % of cell viability in the cryopreserved beads was measured (using the triphenyl tetrazolium method), which corresponded to vigorous growth of 100 % of beads after culture on semi-solid medium. The cryopreserved encapsulated cells were successfully used for initiation of new cell suspensions and their embryogenic capacity was studied. This cryopreservation method is an advance to store ready-to-use competent embryogenic tissue for grapevine genetic transformation projects

Group theoretical Quantization of Isotropic Loop Cosmology

We achieve a group theoretical quantization of the flat Friedmann-Robertson-Walker model coupled to a massless scalar field adopting the improved dynamics of loop quantum cosmology. Deparemeterizing the system using the scalar field as internal time, we first identify a complete set of phase space observables whose Poisson algebra is isomorphic to the su(1,1) Lie algebra. It is generated by the volume observable and the Hamiltonian. These observables describe faithfully the regularized phase space underlying the loop quantization: they account for the polymerization of the variable conjugate to the volume and for the existence of a kinematical non-vanishing minimum volume. Since the Hamiltonian is an element in the su(1,1) Lie algebra, the dynamics is now implemented as SU(1,1) transformations. At the quantum level, the system is quantized as a time-like irreducible representation of the group SU(1,1). These representations are labeled by a half-integer spin, which gives the minimal volume. They provide superselection sectors without quantization anomalies and no factor ordering ambiguity arises when representing the Hamiltonian. We then explicitly construct SU(1,1) coherent states to study the quantum evolution. They not only provide semiclassical states but truly dynamical coherent states. Their use further clarifies the nature of the bounce that resolves the big bang singularity.Comment: 33 pages, v2: some references updated and added, minor changes in the introductio