Quantum Gravity coupled to Matter via Noncommutative Geometry

We show that the principal part of the Dirac Hamiltonian in 3+1 dimensions emerges in a semi-classical approximation from a construction which encodes the kinematics of quantum gravity. The construction is a spectral triple over a configuration space of connections. It involves an algebra of holonomy loops represented as bounded operators on a separable Hilbert space and a Dirac type operator. Semi-classical states, which involve an averaging over points at which the product between loops is defined, are constructed and it is shown that the Dirac Hamiltonian emerges as the expectation value of the Dirac type operator on these states in a semi-classical approximation.Comment: 15 pages, 1 figur

Genetic Family and Stock Type Influence Simulated Loblolly Pine Yields from Wet Sites

Planting adapted families or a bulked seedlot of bare-root and container-grown-seedlings of loblolly pine (Pinus taeda L) were contrasted as cost effective alternatives for regenerating Arkansas\u27 wet sites. Survival data from two wet sites were used to simulate 15 years of growth. Containerized seedlings provided 17% greater survival than bare-root seedlings, but yielded a lower present net worth than bare-root seedlings. Planting families adapted to excessive moisture provided 7% greater survival and yielded a greater present net worth than planting a bulked seedlot consisting of adapted and poorly adapted families

Quasi-Dirac Operators and Quasi-Fermions

We investigate examples of quasi-spectral triples over two-dimensional commutative sphere, which are obtained by modifying the order-one condition. We find equivariant quasi-Dirac operators and prove that they are in a topologically distinct sector than the standard Dirac operator.Comment: 11 page

On Semi-Classical States of Quantum Gravity and Noncommutative Geometry

We construct normalizable, semi-classical states for the previously proposed model of quantum gravity which is formulated as a spectral triple over holonomy loops. The semi-classical limit of the spectral triple gives the Dirac Hamiltonian in 3+1 dimensions. Also, time-independent lapse and shift fields emerge from the semi-classical states. Our analysis shows that the model might contain fermionic matter degrees of freedom. The semi-classical analysis presented in this paper does away with most of the ambiguities found in the initial semi-finite spectral triple construction. The cubic lattices play the role of a coordinate system and a divergent sequence of free parameters found in the Dirac type operator is identified as a certain inverse infinitesimal volume element.Comment: 31 pages, 10 figure

Finding the Standard Model of Particle Physics, A Combinatorial Problem

We present a combinatorial problem which consists in finding irreducible Krajewski diagrams from finite geometries. This problem boils down to placing arrows into a quadratic array with some additional constrains. The Krajewski diagrams play a central role in the description of finite noncommutative geometries. They allow to localise the standard model of particle physics within the set of all Yang-Mills-Higgs models

HS Hya about to turn off its eclipses

Aims: We aim to perform the first long-term analysis of the system HS Hya. Methods: We performed an analysis of the long-term evolution of the light curves of the detached eclipsing system HS Hya. Collecting all available photometric data since its discovery, the light curves were analyzed with a special focus on the evolution of system's inclination. Results: We find that the system undergoes a rapid change of inclination. Since its discovery until today the system's inclination changed by more than 15 deg. The shape of the light curve changes, and now the eclipses are almost undetectable. The third distant component of the system is causing the precession of the close orbit, and the nodal period is about 631 yr. Conclusions: New precise observations are desperately needed, preferably this year, because the amplitude of variations is decreasing rapidly every year. We know only 10 such systems on the whole sky at present.Comment: 4 pages, 3 figures, published in 2012A&A...542L..23

Spin Foams and Noncommutative Geometry

We extend the formalism of embedded spin networks and spin foams to include topological data that encode the underlying three-manifold or four-manifold as a branched cover. These data are expressed as monodromies, in a way similar to the encoding of the gravitational field via holonomies. We then describe convolution algebras of spin networks and spin foams, based on the different ways in which the same topology can be realized as a branched covering via covering moves, and on possible composition operations on spin foams. We illustrate the case of the groupoid algebra of the equivalence relation determined by covering moves and a 2-semigroupoid algebra arising from a 2-category of spin foams with composition operations corresponding to a fibered product of the branched coverings and the gluing of cobordisms. The spin foam amplitudes then give rise to dynamical flows on these algebras, and the existence of low temperature equilibrium states of Gibbs form is related to questions on the existence of topological invariants of embedded graphs and embedded two-complexes with given properties. We end by sketching a possible approach to combining the spin network and spin foam formalism with matter within the framework of spectral triples in noncommutative geometry.Comment: 48 pages LaTeX, 30 PDF figure