Complex geometry,unification, and quantum gravity. I. The geometry of elementary particles

The Poincaré group is replaced byU(3, 2), the pseudounitary extension of the de Sitter groupSO(3, 2), as internal and space-time symmetries are combined in a geometric setting which invalidates the no-go theorems. A new model of elementary particles as vertical vectors on the principal fiber bundleU(3, 2) U(3, 2)/U(3, 1)×U(1) is introduced and their interactions via Lie bracket analyzed. The model accounts for the four known superselection rules: spin, electric charge, baryon number, and lepton number.     

Physical continuum and the problem of a finitistic quantum field theory

To formulate a finitistic quantum field theory, the hypothesis is made that the continuum of space and time is countable possessing the cardinal number ₀. With the integers having the same cardinal number, it is therefore assumed that distances in space and time can be expressed only in integer multiples of a fundamental length and time. To preserve the condition of causality, a quantized field theory derived under this assumption must be expressed in absolute space and time, with the field equation invariant under Galilei transformations. It is shown that such a theory not only can be formulated in full agreement with all the postulates of quantum mechanics, but that it leads to Lorentz invariance as a dynamic symmetry in the limit of low energies. If the smallest length and time are chosen to be equal to the Planck length and time, respectively, observable departures from the predictions of special relativity would become effective only in approaching the Planck energy of 10¹⁹ GeV.     

Vibrational transitions in the non-linearly driven oscillator: role of a time-varying frequency

An operator-algebraic approach is used to study the role of time-varying frequency in vibrational transitions in molecular collisions. The time-evolution operator is constructed in terms of the number, one-quantum, and direct two-quantum operators. The evolution of vibrational states in a homonuclear diatomic molecule forced by an incident particle of the same mass is presented. The effect of the time-dependent frequency on 0 → 1, O → 2, and 0 → 3 is found to be important over a wide range of collision energies. Two-quantum processes interfere destructively with one-quantum processes at lower energies but constructively at higher energies.     

Low-energy nondipole effects in molecular nitrogen valence-shell photoionization

Observations are reported for the first time of significant nondipole effects in the photoionization of the outer-valence orbitals of diatomic molecules. Measured nondipole angular-distribution parameters for the 3sigma(g), 1pi(u), and 2sigma(u) shells of N2 exhibit spectral variations with incident photon energies from thresholds to approximately 200 eV which are attributed via concomitant calculations to particular final-state symmetry waves arising from (E1)multiply sign in circle(M1,E2) radiation-matter interactions first-order in photon momentum. Comparisons with previously reported K-edge studies in N2 verify linear scaling with photon momentum, accounting in part for the significantly enhanced nondipole behavior observed in inner-shell ionization at correspondingly higher momentum values in this molecule.     

Recreational runners with patellofemoral pain exhibit elevated patella water content

Increased bone water content resulting from repetitive patellofemoral joint overloading has been suggested to be a possible mechanism underlying patellofemoral pain (PFP). To date, it remains unknown whether persons with PFP exhibit elevated bone water content. The purpose of this study was to determine whether recreational runners with PFP exhibit elevated patella water content when compared to pain-free controls. Ten female recreational runners with a diagnosis of PFP (22 to 39 years of age) and 10 gender, age, weight, height, and activity matched controls underwent chemical-shift-encoded water-fat magnetic resonance imaging (MRI) to quantify patella water content (i.e., water-signal fraction). Differences in bone water content of the total patella, lateral aspect of the patella, and medial aspect of the patella were compared between groups using independent t tests. Compared with the control group, the PFP group demonstrated significantly greater total patella bone water content (15.4 ± 3.5% vs. 10.3 ± 2.1%; P = 0.001), lateral patella water content (17.2 ± 4.2% vs. 11.5 ± 2.5%; P = 0.002), and medial patella water content (13.2 ± 2.7% vs. 8.4 ± 2.3%; P < 0.001). The higher patella water content observed in female runners with PFP is suggestive of venous engorgement and elevated extracellular fluid. In turn, this may lead to an increase in intraosseous pressure and pain.     

Crystalline and random “diamond-like” boron–carbon structures

The bulk properties and relative stabilities of B–C structures are studied using both first-principles and molecular dynamics simulations that employ Tersoff potentials. The elastic properties of the B–C structures are deduced and some properties of random structures compared with possible crystalline counterparts.     

A new blue-emitting phosphor, SrZnO2:Pb, synthesized by the adipic acid templated sol-gel route

A new blue-emitting phosphor, Sr_1−xPb_xZnO₂, was prepared by a novel adipic acid templated sol-gel route. Photoluminescence and crystalline properties were investigated as functions of calcination temperatures and the Pb²⁺ doping levels. It was found that under UV excitation with a wavelength of 283 or 317 nm, the phosphors gave emission from 374 to 615 nm with a peak centered at 451 nm. This broad-band was composed of UV and the visible range was attributed to an impurity-trapped exciton-type emission. The maximum emission intensity of the Sr_1−xPb_xZnO₂ phosphors occurred at a Pb concentration of x=0.01. The decay time was observed to be ∼33 ms for the compound doped with 1 mol% Pb prepared at 1000 °C. Diffuse reflectance spectra revealed the characteristic absorption peaks and the bandgap energy of SrZnO₂ was found to be 3.4 eV. SEM analysis indicated that phosphor particles have an irregularly rounded morphology and the average particle size was found to be approximately 1 μm.     

Dilatation transformation and sum rules for general potentials including self-consistent field potentials

The eigenfunctions and energies of general dilated Hamiltonians are expanded in powers of the dilatation parameter. These expansions, augmented by stationarity and stability conditions, are used to derive exact sum rules for bound and resonance states. Particular attention is paid to Hamiltonians with potentials which depend on external parameters, such as the nuclear coordinates in molecules, and to self-consistent potentials. The sum rules can be employed in practical computations to improve the quality of the results and may also serve in analyzing the results from approximate calculations.