Geometrization of the physics with teleparallelism. I. The classical interactions

A connection viewed from the perspective of integration has the Bianchi identities as constraints. It is shown that the removal of these constraints admits a natural solution on manifolds endowed with a metric and teleparallelism. In the process, the equations of structure and the Bianchi identities take standard forms of field equations and conservation laws.The Levi-Civita (part of the) connection ends up as the potential for the gravity sector, where the source is geometric and tensorial and contains an explicit gravitational contribution.Nonlinear field equations for the torsion result. In a low-energy approximation (linearity andlow energy-momentumtransfer), the postulate that only charge and velocities contribute to the source transforms these equations into the Maxwell system. Moreover, the affine geodesics become the equations of motion of special relativity with Lorentz force in the same approximation [J. G. Vargas,Found. Phys. 21, 379 (1991)]. The field equations for the torsion must then be viewed as applying to an electromagnetic/strong interaction.A classical unified theory thus arises where the underlying geometry confers their contrasting characters to Maxwell-Lorentz electrodynamics and to an Einstein's-like theory of gravity. The highly compact field equations must, however, be developed in phase-spacetime, since the connection is velocity-dependent, i.e., Finsler-like.Further opportunities for similarities with present-day physics are discussed: (a) teleparallelism allows for the formulation of the torsion sector of the theory as a flat space theory with concomitant point-dependent transformations; (b) spinors should replace Lorentz frames in their role as the subjects to which the connection refers; (c) the Dirac equation consistent with the frame bundle for a velocity-dependent metric with Lorentz signature generates a weak-like interaction in the torsion sector.Work done at the Department of Mathematics and Physics of the Interamerican University of Puerto Rico, San German, Puerto Rico 00683.     

The semiclassical limit of a quantum Fermi accelerator

A classical Fermi accelerator model (FAM) is known to show chaotic behavior. The FAM is defined by a free particle bouncing elastically from two rigid walls, one fixed and the other oscillating periodically in time. The central aim of this paper is to connect the quantum and the classical solutions to the FAM in the semiclassical limit. This goal is accomplished using a finite inverted parametric oscillator (FIPO), confined to a box withfixed walls, as an alternative representation of the FAM. In the FIPO representation, an explicit correspondence between classical and quantum limits is accomplished using a Husimi representation of the quasienergy eigenfunctions.     

The Hamiltonian constraint in the teleparallel equivalent of general relativity

In the teleparallel equivalent of general relativity the integral form of the Hamiltonian constraint contains explicitly theadm energy in the case of asymptotically flat space-times. We show that such expression of the constraint leads to a natural and straightforward construction of a Schrödinger equation for time-dependent physical states. The quantized Hamiltonian constraint is thus written as an energy eigenvalue equation. We further analyse the constraint equations in the case of a space-time endowed with a spherically symmetric geometry. We find the general functional form of the time-dependent solutions of the quantized Hamiltonian and vector constraints.     

Morphology of the male reproductive system and spermatozoa in Centris Fabricius, 1804 (Hymenoptera: Apidae, Centridini)

The genera Centris and Epicharis constitute the Centridini and are widely distributed in the Neotropical region. Centris is also found in the southern portion of the Neartic region, although both genera are more abundant in the humid tropical regions. To describe the structure of the male reproductive system and spermatozoa, light and transmission electron microscopy were used. The male reproductive system of Centris sp. is formed by a pair of testes, a pair of deferent ducts, a pair of seminal vesicles, a pair of accessory glands and an ejaculatory duct connected to the external genitalia, the aedeagus. In this species, testes and the pre-vesicular deferens ducts as well as the seminal vesicles are encapsulated in a single conjunctive capsule, the scrotal membrane. Each testis consists of four testicular follicles, made up of cysts with up to 64 germinative cells. Histologically, the seminal vesicles are formed by a simple cylindrical epithelium, basal membrane and muscular tunic. The spermatozoa of Centris analis, C. fuscata, C. tarsata and Centris sp. are morphologically similar. They have two easily distinguishable regions: the head and flagellum. The head is formed by the two-layer acrosome, the linear nucleus and the flagellum, the centriole adjunct, the axoneme of pattern 9+9+2 microtubules, two asymmetric mitochondrial derivatives and two accessory bodies. These Centris species share various morphological characteristics of the male reproductive system and spermatozoa with the other bees previously described, indicating that several characteristics are synapomorphic for the family Apidae. Studies on the morphology of the male reproductive system and spermatozoa in Hymenoptera have demonstrated the diversity of the information provided by these reproductive structures, which can be used in taxonomy studies and the phylogeny of this important group of insects.     

Nanocrystalline CoSn2-carbon composite electrode prepared by using sonochemistry

A sonochemical method has been used to prepare negative electrode materials containing intermetallic nanoparticles and polyacrylonitrile (PAN). The ultrasound irradiation is applied to achieve small particle size. After annealing at 490 °C under Ar-flow, the polymer PAN is partially carbonized and the metallic nanoparticles are surrounded by a carbonaceous matrix. The main metallic phase is CoSn₂. The carbonaceous coating and the surface oxides have been explored by using XPS. The resulting CoSn₂-carbonaceous phase electrode (CoSn₂@C) shows improved electrochemical behavior (ca. 450 mAh/g after 50 cycles) in comparison with previous reports on pure crystalline CoSn₂. The reaction between CoSn₂@C and Li has been studied by using XRD and ¹¹⁹Sn Mössbauer spectroscopy. The formation of large grains of crystalline Li_xSn phases after the first discharge is discarded. The small particle size which is achieved by using ultrasonication and the carbonaceous matrix contribute to maintain the Co-Sn interactions during the electrochemical cycling. The aggregation of the nanosized metallic particles upon electrochemical cycling can be suppressed by the carbonaceous matrix (pyrolytic PAN).     

Antiferromagnetic Potts Models on the Square Lattice: A High-Precision Monte Carlo Study

We study the antiferromagnetic q-state Potts model on the square lattice for q=3 and q=4, using the Wang–Swendsen–Kotecký (WSK) Monte Carlo algorithm and a powerful finite-size-scaling extrapolation method. For q=3 we obtain good control up to correlation length 5000; the data are consistent with ()=Ae ^{2 p} (1+a ₁ e ^– + ...) as , with p1. The staggered susceptibility behaves as _stagg ^5/3. For q=4 the model is disordered (2) even at zero temperature. In appendices we prove a correlation inequality for Potts antiferromagnets on a bipartite lattice, and we prove ergodicity of the WSK algorithm at zero temperature for Potts antiferromagnets on a bipartite lattice.