We study the quantum deformation of the Barrett-Crane Lorentzian spin foam model which is conjectured to be the discretization of Lorentzian Plebanski model with positive cosmological constant and includes therefore as a particular sector quantum gravity in de-Sitter space. This spin foam model is constructed using harmonic analysis on the quantum Lorentz group. The evaluation of simple spin ne...

The index bundle of the Overlap lattice Dirac operator over the orbit space of lattice gauge fields is introduced and studied. Obstructions to the vanishing of gauge anomalies in the Overlap formulation of lattice chiral gauge theory have a natural description in this context. Our main result is a formula for the topological charge (Pontryargin number) of the index bundle over evendimensional s...

Using Fefferman's analysis of the quantum electron-proton gas, we give a rigorous proof of ionization equilibrium in this system. Ionization equilibrium phases are obtained as low-density and low-temperature limits, letting the chemical potential #(T) approach the ground-state energy of the hydrogen atom as the temperature T tends to zero. The rate of ionization is determined by the slope of #(...

The index bundle of the Overlap lattice Dirac operator over the orbit space of lattice gauge fields is introduced and studied. Obstructions to the vanishing of gauge anomalies in the Overlap formulation of lattice chiral gauge theory have a natural description in this context. Our main result is a formula for the topological charge (Pontryargin number) of the index bundle over evendimensional s...

I present a weak lensing sensitivity estimate for upcoming high redshift (epoch of reionization and beyond) 21cm surveys. Instruments such as PAST, LOFAR and SKA should be able to measure the weak lensing power spectrum to precisions far exceeding conceivable optical surveys. Three types of sources are detectable, which include the re-ionization stromgren spheres, large scale structure, and min...

The index bundle of the Overlap lattice Dirac operator over the orbit space of lattice gauge fields is introduced and studied. Obstructions to the vanishing of gauge anomalies in the Overlap formulation of lattice chiral gauge theory have a natural description in this context. Our main result is a formula for the topological charge (integrated Chern character) of the index bundle over evendimen...

The index bundle of the Overlap lattice Dirac operator over the orbit space of lattice gauge fields is introduced and studied. Obstructions to the vanishing of gauge anomalies in the Overlap formulation of lattice chiral gauge theory have a natural description in this context. Our main result is a formula for the topological charge (Pontryargin number) of the index bundle over evendimensional s...

Incidentally, the value of p obtained in (9) shows that the torsion, unlike the curvature, is independent of v. An arbitrary field of force (1) produces oo trajectories, of which oo pass through a given point in a given direction. These oo trajectories have, at the given point, a common osculating plane and a common torsion. The locus of centers of their osculating spheres is a straight line. T...

It was recently shown by R. Souam and E. Toubiana [33] that the (non constantly curved) Berger spheres do not contain totally umbilic surfaces. Nevertheless in this article we show, by perturbative arguments, that all analytic metrics su ciently close to the round metric g0 on S possess generalized totally umbilic 2-spheres, namely critical points of the conformal Willmore functional ∫ Σ |A◦|2 ...

Quantum super 2-shpheres and the corresponding quantum super transformation group are introduced in analogy to the well-known quantum 2-shpheres and quantum SL(2), connection between little t-Jacobi polynomials and the finite dimensional representations of the quantum super group is formulated, and the Peter-Weyl theorem is obtained. The quantum group SUq(2) introduced by Woronowicz and the qua...