Bi-Hamiltonian Structure of the Supersymmetric Nonlinear Schrodinger Equation

We show that the supersymmetric nonlinear Schr\"odinger equation is a bi-Hamiltonian integrable system. We obtain the two Hamiltonian structures of the theory from the ones of the supersymmetric two boson hierarchy through a field redefinition. We also show how the two Hamiltonian structures of the supersymmetric KdV equation can be derived from a Hamiltonian reduction of the supersymmetric two boson hierarchy as well.Comment: 13 pages, plain Te

Improving LMA predictions with non standard interactions

It has been known for some time that the well established LMA solution to the observed solar neutrino deficit fails to predict a flat energy spectrum for SuperKamiokande as opposed to what the data indicates. It also leads to a Chlorine rate which appears to be too high as compared to the data. We investigate the possible solution to these inconsistencies with non standard neutrino interactions, assuming that they come as extra contributions to the $\nu_{\alpha}\nu_{\beta}$ and $\nu_{\alpha}e$ vertices that affect both the propagation of neutrinos through solar matter and their detection. We find that, among the many possibilities for non standard couplings, only one of them leads to a flat SuperKamiokande spectral rate in better agreement with the data and predicts a Chlorine rate within 1$\sigma$ of the observed one, while keeping all other predictions accurate

Quantum aether and an invariant Planck scale

We argue that a quantum aether is consistent with the principle of relativity and can provide an economical way of having an invariant quantum gravity or Planck scale. We also show that it may change the effective scale at which quantum gravity effects may be observable.Comment: 3 pages, LaTeX, no figures, to appear in EP

Integrable Models and the Higher Dimensional Representations of Graded Lie Algebras

We construct a zero curvature formulation, in superspace, for the sTB-B hierarchy which naturally reduces to the zero curvature condition in terms of components, thus solving one of the puzzling features of this model. This analysis, further, suggests a systematic method of constructing higher dimensional representations for the zero curvature condition starting with the fundamental representation. We illustrate this with the examples of the sTB hierarchy and the sKdV hierarchy. This would be particularly useful in constructing explicit higher dimensional representations of graded Lie algebras.Comment: 13 pages, late