Expansions of algebras and superalgebras and some applications

After reviewing the three well-known methods to obtain Lie algebras and superalgebras from given ones, namely, contractions, deformations and extensions, we describe a fourth method recently introduced, the expansion of Lie (super)algebras. Expanded (super)algebras have, in general, larger dimensions than the original algebra, but also include the Inonu-Wigner and generalized IW contractions as a particular case. As an example of a physical application of expansions, we discuss the relation between the possible underlying gauge symmetry of eleven-dimensional supergravity and the superalgebra osp(1|32).Comment: Invited lecture delivered at the 'Deformations and Contractions in Mathematics and Physics Workshop', 15-21 January 2006, Mathematisches Forschungsinstitut Oberwolfach, German

On BPS preons, generalized holonomies and D=11 supergravities

We develop the BPS preon conjecture to analyze the supersymmetric solutions of D=11 supergravity. By relating the notions of Killing spinors and BPS preons, we develop a moving G-frame method (G=GL(32,R), SL(32,R) or Sp(32,R)) to analyze their associated generalized holonomies. As a first application we derive here the equations determining the generalized holonomies of k/32 supersymmetric solutions and, in particular, those solving the necessary conditions for the existence of BPS preonic (31/32) solutions of the standard D=11 supergravity. We also show that there exist elementary preonic solutions, i.e. solutions preserving 31 out of 32 supersymmetries in a Chern--Simons type supergravity. We present as well a family of worldvolume actions describing the motion of pointlike and extended BPS preons in the background of a D'Auria-Fre type OSp(1|32)-related supergravity model. We discuss the possible implications for M-theory.Comment: 11 pages, RevTeX Typos corrected, a short note and references adde

Spin structure of the nucleon at low energies

The spin structure of the nucleon is analyzed in the framework of a Lorentz-invariant formulation of baryon chiral perturbation theory. The structure functions of doubly virtual Compton scattering are calculated to one-loop accuracy (fourth order in the chiral expansion). We discuss the generalization of the Gerasimov-Drell-Hearn sum rule, the Burkhardt-Cottingham sum rule and moments of these. We give predictions for the forward and the longitudinal-transverse spin polarizabilities of the proton and the neutron at zero and finite photon virtuality. A detailed comparison to results obtained in heavy baryon chiral perturbation theory is also given.Comment: 29 pp, 14 fig

Ab initio Quantum and ab initio Molecular Dynamics of the Dissociative Adsorption of Hydrogen on Pd(100)

The dissociative adsorption of hydrogen on Pd(100) has been studied by ab initio quantum dynamics and ab initio molecular dynamics calculations. Treating all hydrogen degrees of freedom as dynamical coordinates implies a high dimensionality and requires statistical averages over thousands of trajectories. An efficient and accurate treatment of such extensive statistics is achieved in two steps: In a first step we evaluate the ab initio potential energy surface (PES) and determine an analytical representation. Then, in an independent second step dynamical calculations are performed on the analytical representation of the PES. Thus the dissociation dynamics is investigated without any crucial assumption except for the Born-Oppenheimer approximation which is anyhow employed when density-functional theory calculations are performed. The ab initio molecular dynamics is compared to detailed quantum dynamical calculations on exactly the same ab initio PES. The occurence of quantum oscillations in the sticking probability as a function of kinetic energy is addressed. They turn out to be very sensitive to the symmetry of the initial conditions. At low kinetic energies sticking is dominated by the steering effect which is illustrated using classical trajectories. The steering effects depends on the kinetic energy, but not on the mass of the molecules. Zero-point effects lead to strong differences between quantum and classical calculations of the sticking probability. The dependence of the sticking probability on the angle of incidence is analysed; it is found to be in good agreement with experimental data. The results show that the determination of the potential energy surface combined with high-dimensional dynamical calculations, in which all relevant degrees of freedon are taken into account, leads to a detailed understanding of the dissociation dynamics of hydrogen at a transition metal surface.Comment: 15 pages, 9 figures, subm. to Phys. Rev.

Universal Correlations in Pion-less EFT with the Resonating Group Model: Three and Four Nucleons

The Effective Field Theory "without pions" at next-to-leading order is used to analyze universal bound state and scattering properties of the 3- and 4-nucleon system. Results of a variety of phase shift equivalent nuclear potentials are presented for bound state properties of 3H and 4He, and for the singlet S-wave 3He-neutron scattering length a_0(3He-n). The calculations are performed with the Refined Resonating Group Method and include a full treatment of the Coulomb interaction and the leading-order 3-nucleon interaction. The results compare favorably with data and values from AV18(+UIX) model calculations. A new correlation between a_0(3He-n) and the 3H binding energy is found. Furthermore, we confirm at next-to-leading order the correlations, already found at leading-order, between the 3H binding energy and the 3H charge radius, and the Tjon line. With the 3H binding energy as input, we get predictions of the Effective Field Theory "without pions" at next-to-leading order for the root mean square charge radius of 3H of (1.6\pm 0.2) fm, for the 4He binding energy of (28\pm 2.5) MeV, and for Re(a_0(3He-n)) of (7.5\pm 0.6)fm. Including the Coulomb interaction, the splitting in binding energy between 3H and 3He is found to be (0.66\pm 0.03) MeV. The discrepancy to data of (0.10\mp 0.03) MeV is model independently attributed to higher order charge independence breaking interactions. We also demonstrate that different results for the same observable stem from higher order effects, and carefully assess that numerical uncertainties are negligible. Our results demonstrate the convergence and usefulness of the pion-less theory at next-to-leading order in the 4He channel. We conclude that no 4-nucleon interaction is needed to renormalize the theory at next-to-leading order in the 4-nucleon sector.Comment: 24 pages revtex4, including 8 figures as .eps files embedded with includegraphicx, leading-order results added, calculations include the LO three-nucleon interaction explicitly, comment on Wigner bound added, minor modification

Universality in the Three-Body Problem for 4He Atoms

The two-body scattering length a for 4He atoms is much larger than their effective range r_s. As a consequence, low-energy few-body observables have universal characteristics that are independent of the interaction potential. Universality implies that, up to corrections suppressed by r_s/a, all low-energy three-body observables are determined by a and a three-body parameter \Lambda_*. We give simple expressions in terms of a and \Lambda_* for the trimer binding energy equation, the atom-dimer scattering phase shifts, and the rate for three-body recombination at threshold. We determine \Lambda_* for several 4He potentials from the calculated binding energy of the excited state of the trimer and use it to obtain the universality predictions for the other low-energy observables. We also use the calculated values for one potential to estimate the effective range corrections for the other potentials.Comment: 23 pages, revtex4, 6 ps figures, references added, universal expressions update

Use of the Generalized Gradient Approximation in Pseudopotential Calculations of Solids

We present a study of the equilibrium properties of $sp$-bonded solids within the pseudopotential approach, employing recently proposed generalized gradient approximation (GGA) exchange correlation functionals. We analyze the effects of the gradient corrections on the behavior of the pseudopotentials and discuss possible approaches for constructing pseudopotentials self-consistently in the context of gradient corrected functionals. The calculated equilibrium properties of solids using the GGA functionals are compared to the ones obtained through the local density approximation (LDA) and to experimental data. A significant improvement over the LDA results is achieved with the use of the GGA functionals for cohesive energies. For the lattice constant, the same accuracy as in LDA can be obtained when the nonlinear coupling between core and valence electrons introduced by the exchange correlation functionals is properly taken into account. However, GGA functionals give bulk moduli that are too small compared to experiment.Comment: 15 pages, latex, no figure

Palaeobiology, ecology, and distribution of stromatoporoid faunas in biostromes of the mid-Ludlow of Gotland

Six well exposed mid−Ludlow stromatoporoid−dominated reef biostromes in four localities from the Hemse Group in southeastern Gotland, Sweden comprise a stromatoporoid assemblage dominated by four species; Clathrodictyon mohicanum, “Stromatopora” bekkeri, Plectostroma scaniense, and Lophiostroma schmidtii. All biostromes investigated in this area (of approximately 30 km2) are interpreted to belong to a single faunal assemblage forming a dense accumulation of fossils that is probably the best exposed stromatoporoid−rich deposit of the Silurian. The results from this comprehensive study strengthen earlier interpretations of a combination of genetic and environmental control on growth−forms of the stromatoporoids. Growth styles are similar for stromatoporoids in all six biostromes. Differences in biostrome fabric are due to variations in the degree of disturbance by storms. The uniformity of facies and the widespread low−diversity fauna support the view that palaeoenvironmental conditions were similar across the area where these biostromes crop out, and promoted the extraordinary growth of stromatoporoids in this shallow shelf area

Universality in Four-Boson Systems

We report recent advances on the study of universal weakly bound four-boson states from the solutions of the Faddeev-Yakubovsky equations with zero-range two-body interactions. In particular, we present the correlation between the energies of successive tetramers between two neighbor Efimov trimers and compare it to recent finite range potential model calculations. We provide further results on the large momentum structure of the tetramer wave function, where the four-body scale, introduced in the regularization procedure of the bound state equations in momentum space, is clearly manifested. The results we are presenting confirm a previous conjecture on a four-body scaling behavior, which is independent of the three-body one. We show that the correlation between the positions of two successive resonant four-boson recombination peaks are consistent with recent data, as well as with recent calculations close to the unitary limit. Systematic deviations suggest the relevance of range corrections.Comment: Accepted for publication in special issue of Few-Body Systems devoted to the Sixth Workshop on the Critical Stability of Quantum Few-Body Systems, October 2011, Erice, Sicily, Ital

Parity violating target asymmetry in electron - proton scattering

We analyze the parity-violating (PV) components of the analyzing power in elastic electron-proton scattering and discuss their sensitivity to the strange quark contributions to the proton weak form factors. We point out that the component of the analyzing power along the momentum transfer is independent of the electric weak form factor and thus compares favorably with the PV beam asymmetry for a determination of the strangeness magnetic moment. We also show that the transverse component could be used for constraining the strangeness radius. Finally, we argue that a measurement of both components could give experimental information on the strangeness axial charge.Comment: 24 pages, Latex, 5 eps figures, submitted to Phys.Rev.