Superintegrability in the Manev Problem and its Real Form Dynamics

We report here the existence of Ermanno-Bernoulli type invariants for the Manev model dynamics which may be viewed upon as remnants of Laplace-Runge-Lenz vector whose conservation is characteristic of the Kepler model. If the orbits are bounded these invariants exist only when a certain rationality condition is met and thus we have superintegrability only on a subset of initial values. We analyze real form dynamics of the Manev model and derive that it is always superintegrable. We also discuss the symmetry algebras of the Manev model and its real Hamiltonian form.Comment: 12 pages, LaTeX, In: Prof. G. Manev's Legacy in Contemporary Astronomy, Theoretical and Gravitational Physics, V. Gerdjikov, M. Tsvetkov (Eds), Heron Press, Sofia 2005, pp. 155-16

Real Hamiltonian forms of Hamiltonian systems

We introduce the notion of a real form of a Hamiltonian dynamical system in analogy with the notion of real forms for simple Lie algebras. This is done by restricting the complexified initial dynamical system to the fixed point set of a given involution. The resulting subspace is isomorphic (but not symplectomorphic) to the initial phase space. Thus to each real Hamiltonian system we are able to associate another nonequivalent (real) ones. A crucial role in this construction is played by the assumed analyticity and the invariance of the Hamiltonian under the involution. We show that if the initial system is Liouville integrable, then its complexification and its real forms will be integrable again and this provides a method of finding new integrable systems starting from known ones. We demonstrate our construction by finding real forms of dynamics for the Toda chain and a family of Calogero--Moser models. For these models we also show that the involution of the complexified phase space induces a Cartan-like involution of their Lax representations.Comment: 15 pages, No figures, EPJ-style (svjour.cls

Neutrino magnetic moments, flavor mixing, and the SuperKamiokande solar data

We find that magnetic neutrino-electron scattering is unaffected by oscillations for vacuum mixing of Dirac neutrinos with only diagonal moments and for Majorana neutrinos with two flavors. For MSW mixing, these cases again obtain, though the effective moments can depend on the neutrino energy. Thus, e.g., the magnetic moments measured with $\bar{\nu}_e$ from a reactor and $\nu_e$ from the Sun could be different. With minimal assumptions, we find a new limit on $\mu_{\nu}$ using the 825-days SuperKamiokande solar neutrino data: $|\mu_{\nu}| \le 1.5\times 10^{-10} \mu_B$ at 90% CL, comparable to the existing reactor limit.Comment: 4 pages including two inline figures. New version has 825 days SK result, some minor revisions. Accepted for Physical Review Letter

Implications of Gallium Solar Neutrino Data for the Resonant Spin-Flavor Precession Scenario

We consider the implications of the recent results of SAGE and GALLEX experiments for the solution of the solar neutrino problem in the framework of the resonant neutrino spin-flavor precession scenario. It is shown that this scenario is consistent with all the existing solar neutrino data including the gallium results. The quality of the fit of the data depends crucially on the magnetic field profile used which makes it possible to get information about the magnetic field in the solar interior. In particular, the magnetic field in the core of the sun must not be too strong ($<3 \times 10^6$ G). The detection rate in the gallium detectors turns out to be especially sensitive to the magnitude of $\Delta m^2$. Predictions for forthcoming solar-neutrino experiments are made.Comment: LaTeX, 16 pages, 5 figures (not included by available upon request by fax or ordinary mail

Effects of neutrino oscillations and neutrino magnetic moments on elastic neutrino-electron scattering

We consider elastic antineutrino-electron scattering taking into account possible effects of neutrino masses and mixing and of neutrino magnetic moments and electric dipole moments. Having in mind antineutrinos produced in a nuclear reactor we compute, in particular, the weak-electromagnetic interference terms which are linear in the magnetic (electric dipole) moments and also in the neutrino masses. We show that these terms are, however, suppressed compared to the pure weak and electromagnetic cross section. We also comment upon the possibility of using the electromagnetic cross section to investigate neutrino oscillations.Comment: 12 pages, REVTEX file, no figures, submitted to Phys.Rev.