Fluctuating dimension in a discrete model for quantum gravity based on the spectral principle

The spectral principle of Connes and Chamseddine is used as a starting point to define a discrete model for Euclidean quantum gravity. Instead of summing over ordinary geometries, we consider the sum over generalized geometries where topology, metric, and dimension can fluctuate. The model describes the geometry of spaces with a countable number n of points, and is related to the Gaussian unitary ensemble of Hermitian matrices. We show that this simple model has two phases. The expectation value , the average number of points in the Universe, is finite in one phase and diverges in the other. We compute the critical point as well as the critical exponent of . Moreover, the space-time dimension delta is a dynamical observable in our model, and plays the role of an order parameter. The computation of is discussed and an upper bound is found, < 2.

Fitting hyperbolic universes to Cayon-Smoot spots in COBE maps

On the possibility that the universe's matter density is low (Ohm(0) < 1), cosmologies can be considered with the metric of Friedmann's open universe but with closed hyperbolic manifolds as the physical three-space. These models have nontrivial spatial topology, with the property of producing multiple images of cosmic sources. Here a fit is attempted of 10 of these models to the physical cold and hot spots found by Cayon & Smoot in the COBE/DMR maps. These spots are interpreted as early, distant images of much nearer sources of inhomogeneity. The source for one of the cold spots is seen as the seed of a known supercluster.

NUMERICAL STUDY OF A PERTURBED EINSTEIN-DESITTER COSMOLOGICAL MODEL

Given the ever-increasing scale of structures discovered in the universe, we solve Einstein's equations numerically, under simplifying assumptions, to examine how this lack of uniformity affects the metric of Einstein-de Sitter cosmology. The results confirm the qualitative conclusion of Barrow, that a large density contrast is compatible with much smaller metric perturbations. The contribution of this peculiar gravity to the redshift might complicate studies of peculiar motions of galaxies, although it appears that the distortion is small for nearby clusters.

Ontogenic development of Guazuma ulmifolia (Sterculiaceae) sapplings

Guazuma ulmifolia is as popular reforestation tree all over Latin America. It is characteristic of the initial stages of the secondary sucession and presents potential utility in the restoring of degraded areas. There is no information about fruit,seed and seedling morphology, which is of fundamental importance for identification, extraction, management and seed germination as well as for the characterization of post-seminal development and normal seedling pattern. To obtain such information, external fruit, and external and internal seed structures were studied considering shape, size, micropile and embryo localization; and tegumentar structures. All stages of this work were conduced in the Universidade Estadual Paulista (UNESP), Campus of Jaboticabal city. The fruits were collected in a mixed plantation in Jaboticabal city, State of São Paulo, Brazil. For the bio metric study eight repetitions of ten fruits and eight repetitions of 100 seeds were utilized. For seed internal traits study, 50 seeds were drenched in a distiled water, cut, and observed with a scanning electron microscope and a stereomicroscope, For post-seminal study ten repetitions of seven seeds were scarificated chemically with sulphuric acid during 50 min, and placed to germinate ina culture medium, at 30 degrees C, and eight hours of photoperiod. We found elipsoid, woody, indehiscent, pentacarpelar fruits, with a mean lenght of 22.61 mm (diameter 24.88 mm) and 64.0 seeds per fruit. Seed shape varies, mean length is 3.07 mm (width of 2.36 mm). The seed is bitegumented, tegmic, with a continuous, axial and curved embryo. The germination is epigeal and the seedlings are fanerocotiledoneus. Drawings of all stages are included.

Symplectic actions on coadjoint orbits

We present a compact expression for the field theoretical actions based on the symplectic analysis of coadjoint orbits of Lie groups. The final formula for the action density α c becomes a bilinear form 〈(S, 1/λ), (y, m y)〉, where S is a 1-cocycle of the Lie group (a schwarzian type of derivative in conformai case), λ is a coefficient of the central element of the algebra and script Y sign ≡ (y, m y) is the generalized Maurer-Cartan form. In this way the action is fully determined in terms of the basic group theoretical objects. This result is illustrated on a number of examples, including the superconformal model with N = 2. In this case the method is applied to derive the N = 2 superspace generalization of the D=2 Polyakov (super-) gravity action in a manifest (2, 0) supersymmetric form. As a byproduct we also find a natural (2, 0) superspace generalization of the Beltrami equations for the (2, 0) supersymmetric world-sheet metric describing the transition from the conformal to the chiral gauge.

Some remarks on the conformal group

It is shown that the local isomorphism between the conformal group of Minkowski spacetime and the group SO(4,2) makes sense only if one eliminates from SO(4,2) one of the Sitter boosts contained in it. © 1992.

HMDSO plasma polymerization and thin film optical properties

Thin films were deposited from hexamethyldisiloxane (HMDSO) in a glow discharge supplied with radiofrequency (rf) power. Actino-metric optical emission spectroscopy was used to follow trends in the plasma concentrations of the species SiH (414.2 nm), CH (431.4 nm), CO (520.0 nm), and H (656.3 nm) as a function of the applied rf power (range 5 to 35 W). Transmission infrared spectroscopy (IRS) was employed to characterize the molecular structure of the polymer, showing the presence of Si-H, Si-O-Si, Si-O-C and C-H groups. The deposition rate, determined by optical interferometry, ranged from 60 to 130 nm/min. Optical properties were determined from transmission ultra violet-visible spectroscopy (UVS) data. The absorption coefficient α, the refractive index n, and the optical gap E04 of the polymer films were calculated as a function of the applied power. The refractive index at a photon energy of 1 eV varied from 1.45 to 1.55, depending on the rf power used for the deposition. The absorption coefficient showed an absorption edge similar to other non-crystalline materials, amorphous hydrogenated carbon, and semiconductors. For our samples, we define as an optical gap, the photon energy E04 corresponding to the energy at an absorption of 104 cm-1. The values of E04 decreased from 5.3 to 4.6 as the rf power was increased from 5 to 35 W. © 1995.

Gravitational Lorentz force and the description of the gravitational interaction

In the context of a gauge theory for the translation group, we have obtained, for a spinless particle, a gravitational analogue of the Lorentz force. Then, we have shown that this force equation can be rewritten in terms of magnitudes related to either the teleparallel or the Riemannian structures induced in spacetime by the presence of the gravitational field. In the first case, it gives a force equation, with torsion playing the role of force. In the second, it gives the usual geodesic equation of general relativity. The main conclusion is that scalar matter is able to feel any one of the above spacetime geometries, the teleparallel and the metric ones. Furthermore, both descriptions are found to be completely equivalent in the sense that they give the same physical trajectory for a spinless particle in a gravitational field.

Do static sources outside a Schwarzschild black hole radiate?

We show that static sources coupled to a massless scalar field in Schwarzschild spacetime give rise to emission and absorption of zero-energy particles due to the presence of Hawking radiation. This is in complete analogy with the description of the bremsstrahlung by a uniformly accelerated charge from the coaccelerated observers' point of view. The response rate of the source is found to coincide with that in Minkowski spacetime as a function of its proper acceleration. It is interesting that this quantum result appears to reflect the classical equivalence principle.

Riemannian and teleparallel descriptions of the scalar field gravitational interaction

A comparative study between the metric and the teleparallel descriptions of gravitation is made for the case of a scalar field. In contrast to the current belief that only spin matter could detect the teleparallel geometry, scalar matter being able to feel the metric geometry only, we show that a scalar field is able not only to feel anyone of these geometries, but also to produce torsion. Furthermore, both descriptions are found to be completely equivalent, which means that in fact, besides coupling to curvature, a scalar field couples also to torsion.

Chiral asymmetry and gravitation theory

In this letter we apply an alternative approach, recently developed, to the description of massless particles of arbitrary spin to the case of spin-two particles. This provides a non-geometrical approach to the theory of linearized gravitation. Within this method the chiral components of a spinor field are treated as independent field variables. The free field Lagrangian is built up from the requirement of chiral invariance. This formulation is parallel to the neutrino theory and leads to a formulation that generalizes, to particles of spin-two, the two-component neutrino theory. At the free field level the analog of curvature tensor, spin connection tensor, and metric tensor are independent quantities. By introducing left-right asymmetric linear interactions of these chiral components we get the linearized gravitation theory.

Interaction of Hawking radiation and a static electric charge

We investigate whether the equality found for the response of static scalar sources interacting (i) with Hawking radiation in Schwarzschild spacetime and (ii) with the Fulling-Davies-Unruh thermal bath in the Rindler wedge is maintained in the case of electric charges. We find a finite result in the Schwarzschild case, which is computed exactly, in contrast with the divergent result associated with the infrared catastrophe in the Rindler case, i.e., in the case of uniformly accelerated charges in Minkowski spacetime. Thus the equality found for scalar sources does not hold for electric charges.

Interaction of Hawking radiation with static sources outside a Schwarzschild black hole

We show that the response rate of (i) a static source interacting with Hawking radiation of a massless scalar field in Schwarzschild spacetime (with the Unruh vacuum) and that of (ii) a uniformly accelerated source with the same proper acceleration in Minkowski spacetime (with the Minkowski vacuum) are equal. We show that this equality will not hold if the Unruh vacuum is replaced by the Hartle-Hawking vacuum. It is verified that the source responds to the Hawking radiation near the horizon as if it were at rest in a thermal bath in Minkowski spacetime with the same temperature. It is also verified that the response rate in the Hartle-Hawking vacuum approaches that in Minkowski spacetime with the same temperature far away from the black hole. Finally, we compare our results with others in the literature.

Low-energy sector quantization of a massless scalar field outside a Reissner-Nordström black hole and static sources

We quantize the low-energy sector of a massless scalar field in Reissner-Nordström spacetime. This allows the analysis of processes involving soft scalar particles occurring outside charged black holes. In particular, we compute the response of a static scalar source interacting with Hawking radiation using the Unruh (and the Hartle-Hawking) vacuum. This response is compared with the one obtained when the source is uniformly accelerated in the usual vacuum of Minkowski spacetime with the same proper acceleration. We show that both responses are in general different in opposition to the result obtained when the Reissner-Nordström black hole is replaced by a Schwarzschild one. The conceptual relevance of this result is commented on. ©2000 The American Physical Society.

Lattice constellations and codes from quadratic number fields

We propose new classes of linear codes over integer rings of quadratic extensions of Q, the field of rational numbers. The codes are considered with respect to a Mannheim metric, which is a Manhattan metric modulo a two-dimensional (2-D) grid. In particular, codes over Gaussian integers and Eisenstein-Jacobi integers are extensively studied. Decoding algorithms are proposed for these codes when up to two coordinates of a transmitted code vector are affected by errors of arbitrary Mannheim weight. Moreover, we show that the proposed codes are maximum-distance separable (MDS), with respect to the Hamming distance. The practical interest in such Mannheim-metric codes is their use in coded modulation schemes based on quadrature amplitude modulation (QAM)-type constellations, for which neither the Hamming nor the Lee metric is appropriate.