The generalized Lichnerowicz formula and analysis of Dirac operators

We study Dirac operators acting on sections of a Clifford module ${\cal E}$\ over a Riemannian manifold $M$. We prove the intrinsic decomposition formula for their square, which is the generalisation of the well-known formula due to Lichnerowicz [L]. This formula enables us to distinguish Dirac operators of simple type. For each Dirac operator of this natural class the local Atiyah-Singer index theorem holds. Furthermore, if $M$\ is compact and {{\petit \rm dim}\;M=2n\ge 4}, we derive an expression for the Wodzicki function $W_{\cal E}$, which is defined via the non-commutative residue on the space of all Dirac operators ${\cal D}({\cal E})$. We calculate this function for certain Dirac operators explicitly. From a physical point of view this provides a method to derive gravity, resp. combined gravity/Yang-Mills actions from the Dirac operators in question.Comment: 25 pages, plain te

Unification of Gravity and Yang-Mills-Higgs Gauge Theories

In this letter we show how the action functional of the standard model and of gravity can be derived from a specific Dirac operator. Far from being exotic this particular Dirac operator turns out to be structurally determined by the Yukawa coupling term. The main feature of our approach is that it naturally unifies the action of the standard model with gravity.Comment: 8 pages, late

Multi-wavelength Observations of Blazar AO 0235+164 in the 2008-2009 Flaring State

The blazar AO 0235+164 (z = 0.94) has been one of the most active objects observed by Fermi Large Area Telescope (LAT) since its launch in Summer 2008. In addition to the continuous coverage by Fermi, contemporaneous observations were carried out from the radio to γ-ray bands between 2008 September and 2009 February. In this paper, we summarize the rich multi-wavelength data collected during the campaign (including F-GAMMA, GASP-WEBT, Kanata, OVRO, RXTE, SMARTS, Swift, and other instruments), examine the cross-correlation between the light curves measured in the different energy bands, and interpret the resulting spectral energy distributions in the context of well-known blazar emission models. We find that the γ-ray activity is well correlated with a series of near-IR/optical flares, accompanied by an increase in the optical polarization degree. On the other hand, the X-ray light curve shows a distinct 20 day high state of unusually soft spectrum, which does not match the extrapolation of the optical/UV synchrotron spectrum. We tentatively interpret this feature as the bulk Compton emission by cold electrons contained in the jet, which requires an accretion disk corona with an effective covering factor of 19% at a distance of 100 R_g. We model the broadband spectra with a leptonic model with external radiation dominated by the infrared emission from the dusty torus

Anisotropies in the diffuse gamma-ray background measured by the Fermi LAT

The contribution of unresolved sources to the diffuse gamma-ray background could induce anisotropies in this emission on small angular scales. We analyze the angular power spectrum of the diffuse emission measured by the Fermi Large Area Telescope at Galactic latitudes |b|>30° in four energy bins spanning 1–50 GeV. At multipoles ℓ≥155, corresponding to angular scales ≲2°, angular power above the photon noise level is detected at >99.99%  confidence level in the 1–2 GeV, 2–5 GeV, and 5–10 GeV energy bins, and at >99% confidence level at 10–50 GeV. Within each energy bin the measured angular power takes approximately the same value at all multipoles ℓ≥155, suggesting that it originates from the contribution of one or more unclustered source populations. The amplitude of the angular power normalized to the mean intensity in each energy bin is consistent with a constant value at all energies, C_P/⟨I⟩^2=9.05±0.84×10^(-6)  sr, while the energy dependence of C_P is consistent with the anisotropy arising from one or more source populations with power-law photon spectra with spectral index Γ_s=2.40±0.07. We discuss the implications of the measured angular power for gamma-ray source populations that may provide a contribution to the diffuse gamma-ray background

Second constant of motion for two-dimensional positronium in a magnetic field

Recent numerical work indicates that the classical motion of positronium in a constant magnetic field does not exhibit chaotic behavior if the system is confined to two dimensions. One would therefore expect this system to possess a second constant of the motion in addition to the total energy. In this paper we construct a generalization of the Laplace-Runge-Lenz vector and show that a component of this vector is a constant of the motion.Comment: 4 pages, no figure

Exploring the Spin Structure of the Proton with Two-Body Partonic Scattering at RHIC

The STAR collaboration at the Relativistic Heavy Ion Collider is using polarized proton beams at sqrt{s} = 200 GeV to study the spin structure of the proton. The first results for the double spin helicity dependence of inclusive jet production are presented along with projections for additional data taken in 2005 and 2006. When fully analyzed these data sets should place strong constraints on the possible contribution of gluonic spin to the proton spin as expressed by Delta G. Future studies using 2-jet or photon-jet coincidences to map out the gluon spin distribution vs. the gluon's momentum fraction of the proton are discussed.Comment: 4 pages, 2 figures, presented at the 18th Int. IUPAP Conf. on Few-Body Problems in Physics, Santos, Sao Paulo, Brazil, August 21-26,200

Dispersion processes

We study a synchronous dispersion process in which $M$ particles are initially placed at a distinguished origin vertex of a graph $G$. At each time step, at each vertex $v$ occupied by more than one particle at the beginning of this step, each of these particles moves to a neighbour of $v$ chosen independently and uniformly at random. The dispersion process ends once the particles have all stopped moving, i.e. at the first step at which each vertex is occupied by at most one particle. For the complete graph $K_n$ and star graph $S_n$, we show that for any constant $\delta>1$, with high probability, if $M \le n/2(1-\delta)$, then the process finishes in $O(\log n)$ steps, whereas if $M \ge n/2(1+\delta)$, then the process needs $e^{\Omega(n)}$ steps to complete (if ever). We also show that an analogous lazy variant of the process exhibits the same behaviour but for higher thresholds, allowing faster dispersion of more particles. For paths, trees, grids, hypercubes and Cayley graphs of large enough sizes (in terms of $M$) we give bounds on the time to finish and the maximum distance traveled from the origin as a function of the number of particles $M$

H2 molecule in strong magnetic fields

The Pauli-Hamiltonian of a molecule with fixed nuclei in a strong constant magnetic field is asymptotic, in norm-resolvent sense, to an effective Hamiltonian which has the form of a multi-particle Schr\"odinger operator with interactions given by one-dimensional \delta-potentials. We study this effective Hamiltonian in the case of the H2 -molecule and establish existence of the ground state. We also show that the inter-nuclear equilibrium distance tends to 0 as the field-strength tends to infinity

Development of a directional bone reaming system.

Preparation of long bones such as the femur or tibia for placement of intramedullary devices for the treatment of fractures usually involves reaming with a series of central cutters driven by a drill-like device with a flexible shaft over a guide wire. The reamers sequentially enlarge the intramedullary canal into a tunnel of circular cross-section and a diameter appropriate for the procedure. The current technology is concentric, meaning that the system is self-centering within the original intramedullary canal and the expansion is symmetric with respect to the original centerline. A novel system for laterally deflecting the head of a 12mm Stryker Bixcut reaming system has been designed in order to test the proof of concept for eccentrically reaming the intramedullary canal of a long bone. Reaming often precedes intramedullary nail placement following a long bone fracture or to induce ankle arthrodesis. Long bones do not always contain a regularly shaped intramedullary canal, thus creating a risk in navigating a reamer through the bone. Pockets of infected tissue and malformed fractures may also create obstacles for advancing a reamer through the canal. The newly developed reaming system is intended to allow the surgeon to be more selective in where the reamer head cuts while shaping the inner wall of the intramedullary canal to avoid or target certain areas of the canal. Development of the directional reaming system included two prototypes with three sets of experiments to quantify the success of the designs. The first experiment resulted in a prototype unable to achieve the specified 3mm of lateral cutting depth. The second experiment also failed to achieve the 3mm of lateral cutting depth, but did yield a proof of concept driving the design of the third iteration. Creation of the third prototype concludes the project with experimentation that was completed in early May of 2017