High Energy Cosmic Tau Neutrinos

I discuss the possibility of production of high energy cosmic tau neutrinos ($E \geq 10^{6}$ GeV) in an astrophysical site and study some of the effects of neutrino mixing on their subsequent propagation. I also discuss the prospects for observations of these high energy cosmic tau neutrinos through double shower events in new km$^{2}$ surface area under water/ice neutrino telescopes.Comment: 3 pages, Latex (uses espcrc2), 1 figure included with epsf, talk given at 6th International Workshop on Topics in Astroparticle and Underground Physics (TAUP 99), 6-10 September, Paris, France [to appear in its proceedings in Nucl. Phys. B (Proc. Suppl.) edited by M. Froissart, J. Dumarchez and D. Vignaud

Ultraviolet behavior in background independent quantum field theory

We describe a background independent quantization of the scalar field that provides an explicit realization of Fock-like states and associated operators in a polymer Hilbert space. The vacuum expectation values of the commutator and anti-commutator of the creation and annihilation operators become energy dependent, and exhibit a surprising transition to fermionic behavior at high energy. Furthermore the approach yields a modified dispersion relation with a leading correction proportional to the momentum cubed. These results suggests a fundamental change in the ultraviolet properties of quantum fields.Comment: 8 pages, 5 figure

The Affine symmetry of self-dual gravity

Self-dual gravity may be reformulated as the two dimensional principal chiral model with the group of area preserving diffeomorphisms as its gauge group. Using this formulation, it is shown that self-dual gravity contains an infinite dimensional hidden symmetry whose generators form the Affine (Kac-Moody) algebra associated with the Lie algebra of area preserving diffeomorphisms. This result provides an observable algebra and a solution generating technique for self-dual gravity.Comment: 20 pages, RevTex, a few presentational changes - version to appear in J. Math. Phy