17 research outputs found

### 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.