Algebraic connections on parallel universes

For any manifold $M$, we introduce a \ZZ -graded differential algebra $\Xi$, which, in particular, is a bi-module over the associative algebra $C(M\cup M)$. We then introduce the corresponding covariant differentials and show how this construction can be interpreted in terms of Yang-Mills and Higgs fields. This is a particular example of noncommutative geometry. It differs from the prescription of Connes in the following way: The definition of $\Xi$ does not rely on a given Dirac-Yukawa operator acting on a space of spinors.Comment: 10 pages, CPT-93/PE 294

Leptonic Generation Mixing, Noncommutative Geometry and Solar Neutrino Fluxes

Triangular mass matrices for neutrinos and their charged partners contain full information on neutrino mixing in a most concise form. Although the scheme is general and model independent, triangular matrices are typical for reducible but indecomposable representations of graded Lie algebras which, in turn, are characteristic for the standard model in noncommutative geometry. The mixing matrix responsible for neutrino oscillations is worked out analytically for two and three lepton families. The example of two families fixes the mixing angle to just about what is required by the Mikheyev-Smirnov-Wolfenstein resonance oscillation of solar neutrinos. In the case of three families we classify all physically plausible choices for the neutrino mass matrix and derive interesting bounds on some of the moduli of the mixing matrix.Comment: LaTeX, 12 page

Sweeping the Space of Admissible Quark Mass Matrices

We propose a new and efficient method of reconstructing quark mass matrices from their eigenvalues and a complete set of mixing observables. By a combination of the principle of NNI (nearest neighbour interaction) bases which are known to cover the general case, and of the polar decomposition theorem that allows to convert arbitrary nonsingular matrices to triangular form, we achieve a parameterization where the remaining freedom is reduced to one complex parameter. While this parameter runs through the domain bounded by a circle with radius R determined by the up-quark masses around the origin in the complex plane one sweeps the space of all mass matrices compatible with the given set of data.Comment: 18 page

Neutrino signatures of supernova shock and reverse shock propagation

A few seconds after bounce in a core-collapse supernova, the shock wave passes the density region corresponding to resonant neutrino oscillations with the ``atmospheric'' neutrino mass difference. The transient violation of the adiabaticity condition manifests itself in an observable modulation of the neutrino signal from a future galactic supernova. In addition to the shock wave propagation effects that were previously studied, a reverse shock forms when the supersonically expanding neutrino-driven wind collides with the slower earlier supernova ejecta. This implies that for some period the neutrinos pass two subsequent density discontinuities, giving rise to a ``double dip'' feature in the average neutrino energy as a function of time. We study this effect both analytically and numerically and find that it allows one to trace the positions of the forward and reverse shocks. We show that the energy dependent neutrino conversion probabilities allow one to detect oscillations even if the energy spectra of different neutrino flavors are the same as long as the fluxes differ. These features are observable in the \bar\nu_e signal for an inverted and in the \nu_e signal for a normal neutrino mass hierarchy, provided the 13-mixing angle is ``large'' (sin^2\theta_{13}\gg 10^{-5}).Comment: 23 pages, 27 eps figures (high resolution plots are available on request), JCAP style; v2: figure 8 extended, matches published versio

Relativistic calculations of pionic and kaonic atoms hyperfine structure

We present the relativistic calculation of the hyperfine structure in pionic and kaonic atoms. A perturbation method has been applied to the Klein-Gordon equation to take into account the relativistic corrections. The perturbation operator has been obtained \textit{via} a multipole expansion of the nuclear electromagnetic potential. The hyperfine structure of pionic and kaonic atoms provide an additional term in the quantum electrodynamics calculation of the energy transition of these systems. Such a correction is required for a recent measurement of the pion mass

Does gravity modelling justify a rifted "Ligurian Basin"?

The geo-historical development of the Ligurian Basin and the structure of the crust and upper mantle in this area are still being discussed. Yet it remains unclear if rifting caused continental break-up and seafloor spreading and one of the key questions is whether rifting can be identified in geophysical measurements. For our investigations we had the following updated data sets at our disposal: the new gravity maps of the AlpArray Gravity Working Group (complete Bouguer - CBA, Free air, and isostatic anomalies) the seismic results of the Lobster campaigns of our GEOMAR partners in the SPP MB4D as well as the dynamic modelling results from our own subproject. The constraining data are supplemented with seismic profile data from French and Italian offshore campaigns, as far as they are usable in publications for us. The GFZ modelling software IGMAS+ was used for an interactive 3D modelling. The resulting model contains density inhomogeneities in the crust as well as in the upper mantle down to a depth of 300 km following the results of dynamic models of our own subproject. Due to the special hybrid modelling of the crust (by polygonal structures) and the upper mantle (by voxels of recent velocity models), the individual contributions to the gravity field are clearly separable. As a further special feature, we point out that the density model used is based on the gravity modelling from the first phase of the SPP MB4D (our former subproject INTEGRATE). Thus, a largely consistent 3D density model for both the Alps and the Ligurian Sea is available for interpretation. The constrained 3D modelling of the gravity field, as well as numerical analyses of the fields (terracing, clustering, filtering, curvature), calculations of the vertical stress and Gravity Potential Energy (GPE) suggest that a rift structure in the area of the Ligurian Sea can be identified and mapped. The interactive modelling is supported by the use of geological maps in the Ligurian Sea area. By overlaying the model gravity maps and the geological maps, the good agreement becomes visible – refer to the attached figure

Confinement limit of Dirac particles in scalar 1D potentials

We present a general proof that Dirac particles cannot be localized below their Compton length by symmetric but otherwise arbitrary scalar potentials. This proof does not invoke the Heisenberg uncertainty relation and thus does not rely on the nonrelativistic linear momentum relation. Further it is argued that the result is also applicable for more general potentials, as e.g. generated by nonlinear interactions. Finally a possible realisation of such a system is proposed.Comment: 2 page

The Interaction of Quantum Gravity with Matter

The interaction of (linearized) gravitation with matter is studied in the causal approach up to the second order of perturbation theory. We consider the generic case and prove that gravitation is universal in the sense that the existence of the interaction with gravitation does not put new constraints on the Lagrangian for lower spin fields. We use the formalism of quantum off-shell fields which makes our computation more straightforward and simpler.Comment: 25 page

Modeling core collapse supernovae in 2 and 3 dimensions with spectral neutrino transport

The overwhelming evidence that the core collapse supernova mechanism is inherently multidimensional, the complexity of the physical processes involved, and the increasing evidence from simulations that the explosion is marginal presents great computational challenges for the realistic modeling of this event, particularly in 3 spatial dimensions. We have developed a code which is scalable to computations in 3 dimensions which couples PPM Lagrangian with remap hydrodynamics [1], multigroup, flux-limited diffusion neutrino transport [2], with many improvements), and a nuclear network [3]. The neutrino transport is performed in a ray-by-ray plus approximation wherein all the lateral effects of neutrinos are included (e.g., pressure, velocity corrections, advection) except the transport. A moving radial grid option permits the evolution to be carried out from initial core collapse with only modest demands on the number of radial zones. The inner part of the core is evolved after collapse along with the rest of the core and mantle by subcycling the lateral evolution near the center as demanded by the small Courant times. We present results of 2-D simulations of a symmetric and an asymmetric collapse of both a 15 and an 11 M progenitor. In each of these simulations we have discovered that once the oxygen rich material reaches the shock there is a synergistic interplay between the reduced ram pressure, the energy released by the burning of the shock heated oxygen rich material, and the neutrino energy deposition which leads to a revival of the shock and an explosion.Comment: 10 pages, 3 figure

Lithospheric density structure of the Southern Central Andes constrained by 3D data-integrative gravity modelling

The southern Central Andes (SCA) (between 27° S and 40° S) is bordered to the west by the convergent margin between the continental South American Plate and the oceanic Nazca Plate. The subduction angle along this margin is variable, as is the deformation of the upper plate. Between 33° S and 35° S, the subduction angle of the Nazca plate increases from subhorizontal (< 5°) in the north to relatively steep (~ 30°) in the south. The SCA contain inherited lithological and structural heterogeneities within the crust that have been reactivated and overprinted since the onset of subduction and associated Cenozoic deformation within the Andean orogen. The distribution of the deformation within the SCA has often been attributed to the variations in the subduction angle and the reactivation of these inherited heterogeneities. However, the possible influence that the thickness and composition of the continental crust have had on both short-term and long-term deformation of the SCA is yet to be thoroughly investigated. For our investigations, we have derived density distributions and thicknesses for various layers that make up the lithosphere and evaluated their relationships with tectonic events that occurred over the history of the Andean orogeny and, in particular, investigated the short- and long-term nature of the present-day deformation processes. We established a 3D model of lithosphere beneath the orogen and its foreland (29° S?39° S) that is consistent with currently available geological and geophysical data, including the gravity data. The modelled crustal configuration and density distribution reveal spatial relationships with different tectonic domains: the crystalline crust in the orogen (the magmatic arc and the main orogenic wedge) is thicker (~ 55 km) and less dense (~ 2900 kg/m3) than in the forearc (~ 35 km, ~ 2975 kg/m3) and foreland (~ 30 km, ~ 3000 kg/m3). Crustal thickening in the orogen probably occurred as a result of stacking of lowdensity domains, while density and thickness variations beneath the forearc and foreland most likely reflect differences in the tectonic evolution of each area following crustal accretion. No clear spatial relationship exists between the density distributio within the lithosphere and previously proposed boundaries of crustal terranes accreted during the early Paleozoic. Areas with ongoing deformation show a spatial correlation with those areas that have the highest topographic gradients and where there are abrupt changes in the average crustal-density contrast. This suggests that the short-term deformation within the interior of the Andean orogen and its foreland is fundamentally influenced by the crustal composition and the relativethickness of different crustal layers. A thicker, denser, and potentially stronger lithosphere beneath the northern part of the SCA foreland is interpreted to have favoured a strong coupling between the Nazca and South American plates, facilitating the development of a sub-horizontal slab.Fil: Rodriguez Piceda, Constanza. German Research Centre for Geosciences; Alemania. Universitat Potsdam; AlemaniaFil: Scheck Wenderoth, Magdalena. German Research Centre for Geosciences; Alemania. RWTH Aachen University; AlemaniaFil: Gómez Dacal, María Laura. German Research Centre for Geosciences; Alemania. Universidad Nacional de La Plata. Facultad de Ciencias Astronómicas y Geofísicas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata; ArgentinaFil: Bott, Judith. German Research Centre for Geosciences; AlemaniaFil: Prezzi, Claudia Beatriz. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Geociencias Básicas, Aplicadas y Ambientales de Buenos Aires. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Geociencias Básicas, Aplicadas y Ambientales de Buenos Aires; ArgentinaFil: Strecker, Manfred R.. German Research Centre for Geosciences; Alemania. Universitat Potsdam; Alemani