New Application of Functional Integrals to Classical Mechanics

In this paper a new functional integral representation for classical dynamics is introduced. It is achieved by rewriting the Liouville picture in terms of bosonic creation-annihilation operators and utilizing the standard derivation of functional integrals for dynamical quantities in the coherent states representation. This results in a new class of functional integrals which are exactly solvable and can be found explicitly when the underlying classical systems are integrable.Comment: 13 page

Minimal See-Saw Model for Atmospheric and Solar Neutrino Oscillations

We present a minimal see-saw model based on an extension of the standard model (SM) which includes an additional U(1), with gauge charge $B - \frac{3}{2} (L_\mu + L_\tau)$. Requirement of anomaly cancellation implies the existence of two right-handed singlet neutrinos, carrying this gauge charge, which have normal Dirac couplings to $\nu_\mu$ and $\nu_\tau$ but suppressed ones to $\nu_e$. Assuming the U(1) symmetry breaking scale to be 10$^{12-16}$~GeV, this model can naturally account for the large (small) mixing solutions to the atmospheric (solar) neutrino oscillations.Comment: 14 pages, latex, no figure