Anomalous Magnetic Moment of W-boson at high temperature

By the Schwinger proper-time method, the one-loop contribution to the anomalous magnetic moment of the W-boson is calculated at high temperature. It is shown that the value of AMM is positive and depends linearly upon temperature

Photon decay gamma->nu anti-nu in an external magnetic field

The process of the photon decay into the neutrino - antineutrino pair in a magnetic field is investigated. The amplitude and the probability are analysed in the limits of relatively small and strong fields. The probability is suppressed by a factor (G_F m^2_e)^2 as compared with the probability of the pure electromagnetic process gamma -> e- e+. However, the process with neutrinos could play a role of an additional channel of stellar energy-loss.Comment: 8 pages, LaTeX, typos fixed, minor modifications, version accepted to Physics Letters

Chaplygin ball over a fixed sphere: explicit integration

We consider a nonholonomic system describing a rolling of a dynamically non-symmetric sphere over a fixed sphere without slipping. The system generalizes the classical nonholonomic Chaplygin sphere problem and it is shown to be integrable for one special ratio of radii of the spheres. After a time reparameterization the system becomes a Hamiltonian one and admits a separation of variables and reduction to Abel--Jacobi quadratures. The separating variables that we found appear to be a non-trivial generalization of ellipsoidal (spheroconical) coordinates on the Poisson sphere, which can be useful in other integrable problems. Using the quadratures we also perform an explicit integration of the problem in theta-functions of the new time.Comment: This is an extended version of the paper to be published in Regular and Chaotic Dynamics, Vol. 13 (2008), No. 6. Contains 20 pages and 2 figure

On bi-hamiltonian structure of some integrable systems on so*(4)

We classify all the quadratic Poisson structures on $so^*(4)$ and $e^*(3)$, which have the same foliation by symplectic leaves as the canonical Lie-Poisson tensors. The separated variables for the some of the corresponding bi-integrable systems are constructed.Comment: LaTeX with Amsfonts, 13 pages, corrected typo

High energy neutrino absorption by W production in a strong magnetic field

An influence of a strong external magnetic field on the neutrino self-energy operator is investigated. The width of the neutrino decay into the electron and W boson, and the mean free path of an ultra-high energy neutrino in a strong magnetic field are calculated. A kind of energy cutoff for neutrinos propagating in a strong field is defined.Comment: 13 pages, LaTeX, 1 EPS figure, submitted to Physics Letters

Plasma influence on the neutrino - electron processes in a strong magnetic field

An influence of the magnetized electron - positron plasma on the absorption and loss of the energy and momentum in a process of neutrino propagation is investigated. A total contribution of all crossed processes, $\nu \to \nu e^- e^+$, $\nu e^- \to \nu e^-$, $\nu e^+ \to \nu e^+$, $\nu e^- e^+ \to \nu$, is found for the first time, which appears not to depend on the chemical potential of electron-positron gas. Relatively simple expressions for the probability and mean losses of the neutrino energy and momentum are obtained, which are suitable for a quantitative analysis.Comment: 8 pages, 1 ps figure, LaTeX, uses espcrc2.sty,epsf.sty, based on the talks presented at the Xth International Baksan School "Particles and Cosmology", Baksan Valley, Kabardino Balkaria, Russia, April 19-25, 1999 and the International Workshop "Particles in Astrophysics and Cosmology: From Theory to Observation", Valencia, Spain, May 3-8, 199

One invariant measure and different Poisson brackets for two nonholonomic systems

We discuss the nonholonomic Chaplygin and the Borisov-Mamaev-Fedorov systems, for which symplectic forms are different deformations of the square root from the corresponding invariant volume form. In both cases second Poisson bivectors are determined by $L$-tensors with non-zero torsion on the configurational space, in contrast with the well known Eisenhart-Benenti and Turiel constructions.Comment: 18 pages, LaTeX with AMSfont

New variables of separation for particular case of the Kowalevski top

We discuss the polynomial bi-Hamiltonian structures for the Kowalevski top in special case of zero square integral. An explicit procedure to find variables of separation and separation relations is considered in detail.Comment: 11 pages, LaTeX with Ams font

A Generalization of Chaplygin's Reducibility Theorem

In this paper we study Chaplygin's Reducibility Theorem and extend its applicability to nonholonomic systems with symmetry described by the Hamilton-Poincare-d'Alembert equations in arbitrary degrees of freedom. As special cases we extract the extension of the Theorem to nonholonomic Chaplygin systems with nonabelian symmetry groups as well as Euler-Poincare-Suslov systems in arbitrary degrees of freedom. In the latter case, we also extend the Hamiltonization Theorem to nonholonomic systems which do not possess an invariant measure. Lastly, we extend previous work on conditionally variational systems using the results above. We illustrate the results through various examples of well-known nonholonomic systems.Comment: 27 pages, 3 figures, submitted to Reg. and Chaotic Dy