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

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

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

Mutational Activation of ras Genes is Absent in Pediatric Osteosarcoma

Activation of ras oncogenes is found in human cancers; overall it is observed in 15% of all neoplasms. The purpose of this study was to assess the extent of involvement of ras oncogenes in osteosarcoma. Tumor samples from a series of 49 pediatric patients diagnosed with osteosarcoma and treated at our institution were evaluated. Paraffin-embedded tumor samples from diagnostic biopsies, from tumor en bloc resection tissue after neoadjuvant chemotherapy, and samples from metastases were examined in search of point mutations in H, K, and N-ras genes at codons 12 and 61 by means of polymerase chain reaction (PCR), slot-blotting, and radioactive labeled specific DNA probes. A total of 92 archival samples were studied. No point mutations activating these genes were found. These findings suggest that the activation by point mutations at codons 12 and 61 of the H, K, and N-ras genes does not play a role in the pathogenesis of human osteosarcoma. Since no point mutations in codons 12 and 61 were detected, it was not possible to establish any correlation between the ras genes and clinical or histologic finding

Fock quantization of a Klein-Gordon field in the interior geometry of a nonrotating black hole

We study the canonical quantization of a scalar field in a Kantowski-Sachs spacetime. For simplicity, we consider compactified spatial sections, since this does not affect the ultraviolet behavior. A time-dependent canonical transformation is performed prior to quantization. As in previously studied cases, the purpose of this canonical transformation is to identify and extract the background contribution to the field evolution which is obstructing a unitary implementation of the field dynamics at the quantum level. This splitting of the time dependence into a background piece and the part to be seen as true quantum evolution is to a large extent determined by the unitarity requirement itself. The quantization is performed in the usual setup of Fock representations, demanding the preservation of the spatial symmetries. Under the joint requirements of quantum unitary dynamics and compatibility with those classical symmetries, the quantization is shown to be unique, in the sense that any two representations with these properties are unitarily equivalent. This confirms the validity of our conditions as criteria to discriminate among possibly inequivalent quantum descriptions. The interest of this analysis goes beyond cosmological applications since the interior of a nonrotating black hole has a geometry of the Kantowski-Sachs type.Comment: 13 page

Cotilos impactados vs. roscados no cementados: estudio radiológico post-operatorio comparativo

Se han valorado radiografías AP de pelvis obtenidas tras colocación de 102 pró- tesis no cementadas en 97 pacientes: 51 eran del tipo cótilo roscado (CR), y 51 del tipo cótilo impactado (CI). Se ha medido el ángulo de inclinación, la posición del cotilo, el grado de centraje, el grado de protrusión/extrusión, y la superficie de contacto entre cótilo y la cavidad acetabular. Globahnente los CR quedan implantados más verticalmente que los CI (p=0,006), así como más lateralizados (p=0,02). El porcentaje de cótilos bien centrados en relación al acetábulo es mayor entre los CI que entre los CR (p=0,002). Un 19% de los CR quedaron parcialmente extraídos, no llegando a contactar con el fondo de la cavidad acetabular, mientras que en ningún caso de los CI se apreció este problema. En conclusión, a pesar de la teórica ventaja de poseer una estabilidad inicial mayor, la orientación de los CR no resulta tan óptima como la obtenida con los CI, lo que asegura una estabilidad mejor a largo plazo y una menor usura del polietileno.—Post-operative anteroposterior radiographs of the pelvis in 102 patients receiving a cementless total hip arthroplasty were analyzed. In a group, a screwed spherical socket (SCR) was applied, while in other a press-fit impacted socket (IMP) was used. The following parameters were studied: inclination angle, location and centering of the acetabular component, degree of protrusion-extrusion, and porcentage of contact surface between the socket and the acetabulum. SCR sockets appeared to be placed more vertically (p=0.006), and laterally (p=0.02) than IMP prostheses. The percent of properly centered sockets was higher among IMP than among SCR implants (p=0.002). SCR prostheses were found to be partly extruded in 19% of cases while none of the IMP prostheses had this problem. In conclussion, despite the theoretical advantage of the SCR implants having a better initial fixation than the IMP implants, the latter tend to be implanted in a more optimal position, thus ensuring a better longterm stability and therefore less wear problems can be expected

Approach to the Spanish continental Neogene synthesis and paleoclimatic interpretation

Integrated studies on Neogene geology have been scarce in Spain, but attemps to stratigraphic and sedimentological analysis of continental Tertiary basins have increased considerably lately. The large extent of Neogene basins in Spain, the good quality of the outcrops and the abundance of fossil provide an excellent basis for this kind of studies

Teratogenicity of zinc deficiency in the rat: study of the fetal skeleton

Zinc deficiency (ZD) is teratogenic in rats, and fetal skeletal defects are prominent. This study identifies fetal skeletal malformations that affect calcified and non-calcified bone tissue as a result of gestational zinc deficiency in rats, and it assesses the effect of maternal ZD in fetal bone calcification. Pregnant Sprague-Dawley rats (180-250 g) were fed 1) a control diet (76.4 micrograms Zn/g diet) ad libitum (group C), 2) a zinc-deficient diet (0 microgram/g) ad libitum (group ZD), or 3) the control diet pair-fed to the ZD rats (group PF). On day 21 of gestation, laparotomies were performed. Fetuses were weighed, examined for external malformations, and stained in toto with a double-staining technique for the study of skeletal malformations. Maternal and fetal tissues were used for Zn, Mg, Ca, and P determinations. Gross external malformations were present in 97% of the ZD fetuses. No external malformations were found in fetuses from groups C and PF. Ninety-one percent of cleared ZD fetuses had multiple skeletal malformations, whereas only 3% of the fetuses of group PF had skeletal defects; no skeletal malformations were found in fetuses from group C. Some of the skeletal malformations described in the ZD fetuses, mainly affecting non-calcified bone, were not mentioned in previous reports, thus stressing the importance of using double-staining techniques. Examination of stained fetuses and counting of ossification centers revealed important calcification defects in ZD fetuses. These effects were confirmed by lower Ca and P concentrations in fetal bone with alteration of the Ca:P ratio

Alterations in deoxyribonucleic acid and proteins in cerebral tissues from fetuses subject to alcohol in utero

Critical period for intra-uterine growth retardation (IUGR), and biochemical parameters for tissue growth were studied in an animal model of Fetal Alcohol Syndrome (FAS) in rats. Our research used 40 animals, fed Lieber and DeCarli liquid diets, distributed into 4 groups: C, or control--non-alcoholic--, ad libitum; E, or alcoholic, fed ad libitum; F, or alcoholic, pair fed to E; and P, non-alcoholic, pair fed to E and F. Fetuses of group E were exposed to ethanol during the organogenic period, while those from group F exposed only during the last stage of pregnancy. Blood alcohol levels were determined both at the end of 42 days before pregnancy, and on days 3, 7, 14 and 19 of gestation. The brain content of total DNA and proteins was measured, along with the cell size of fetal tissues. Non-parametric statistics were applied, considering the litter as unit, and 5% as the significant level. Prenatal ethanol exposure was associated with a cell size, total DNA, and cerebral protein content all significantly lower (p less than or equal to 0.05) than in non-alcoholic groups. These facts strongly suggest that the critical period for growth retardation associated with FAS may be situated at the end of pregnancy, when metabolic disturbances of the brain could also arise, while major external malformations are likely to be produced during organogenesis