Elliptic Algebra and Integrable Models for Solitons on Noncummutative Torus T{\cal T}

We study the algebra ${\cal A}_n$ and the basis of the Hilbert space ${\cal H}_n$ in terms of the $\theta$ functions of the positions of $n$ solitons. Then we embed the Heisenberg group as the quantum operator factors in the representation of the transfer matrice of various integrable models. Finally we generalize our result to the generic $\theta$ case.Comment: Talk given by Bo-Yu Hou at the Joint APCTP-Nankai Symposium. Tianjin (PRC), Oct. 2001. To appear in the proceedings, to be published by Int. J. Mod. Phys. B. 7 pages, latex, no figure

Exotic Neutrino Interactions at the Pierre Auger Observatory

The Pierre Auger Observatory for cosmic rays provides a laboratory for studying fundamental interactions at energies well beyond those available at colliders. In addition to hadrons or photons, Auger is sensitive to ultra-high energy neutrinos in the cosmic radiation and models for new physics can be explored by observing neutrino interactions at center-of-mass energies beyond the TeV scale. By comparing the rate for quasi-horizontal, deeply penetrating air showers triggered by all types of neutrinos with the rate for slightly upgoing showers generated by Earth-skimming tau neutrinos, any deviation of the neutrino-nucleon cross-section from the Standard Model expectation can be constrained. We show that this can test models of low-scale quantum gravity (including processes such as Kaluza-Klein graviton exchange, microscopic black hole production and string resonances), as well as non-perturbative electroweak instanton mediated processes. Moreover, the observed ratios of neutrino flavors would severely constrain the possibility of neutrino decay.Comment: 32 pages (RevTeX); revised to show rates for both the cosmogenic and Waxman-Bahcall neutrino flux; to appear in Astroparticle Physic