International Journal of Modern Physics A

Ultrahigh energy neutrinos can provide important information about the distant astronomical objects and the origin of the Universe. Precise knowledge about neutrino interactions and production rates is essential for estimating background, expected fluxes and detection probabilities. In this paper we review the applications of the high energy QCD to the calculations of the interaction cross-sections of the neutrinos. We also study the production of the ultrahigh energy neutrinos in the atmosphere due to the charm and beauty decays.

The thermal and nonthermal pion production by sigma decay and its relation with chiral symmetry restoration in a hot and dense matter are investigated. The nonthermal decay into pions of sigma mesons which are popularly produced in chiral symmetric phase leads to a low-momentum pion enhancement as a possible signature of chiral phase transition at finite temperature and density.

One approach for solving mechanical problems of constrained systems using the Hamilton–Jacobi formulation is examined. The Hamilton–Jacobi function is obtained in the same manner as for regular systems. This is used to determine the solutions of the equations of motion for constrained systems.

The physical properties of the SO(2, 1) coherent state for the Coulomb problem are discussed in this paper. We find that the coherent state, for which the minimum uncertainty relation holds, has a nonvanishing geometric phase factor, and also is approximately nonspreading in the classical limit of the high excitation of angular momentum.

We propose an action for gravity on a fuzzy sphere, based on a matrix model. We find striking similarities with an analogous model of two-dimensional gravity on a noncommutative plane, i.e. the solution space of both models is spanned by pure U(2) gauge transformations acting on the background solution of the matrix model, and there exist deformations of the classical diffeomorphisms which preserve the two-dimensional noncommutative gravity actions.

In this paper we constructed exact static multimonopole–antimonopole solutions of the YMH field theory. By labelling these solutions as A1, A2, B1, and B2, we notice that the exact axially symmetric 1-monopole — two antimonopoles solution is actually a special case of the A1 solution when the topological index parameter m=1. Also the B1 solution will reduce to a spherically symmetric Wu–Yang type monopole of unit charge when m=0. All these exact solutions satisfy the first order Bogomol'nyi equations and possess infinite energy. Hence they are a different type of the BPS solution. Except for the A1 solution when m=1 and the B1 solution when m=0, these solutions in general do not possess axial symmetry. They represent different combinations of monopoles, multimonopole, and antimonopoles, symmetrically arranged about the z-axis.

A general algebraic condition for the functional independence of 2n-1 constants of motion of an n-dimensional maximal superintegrable Hamiltonian system has been proved for an arbitrary finite n. This makes it possible to construct, in a well-defined generic way, a normalized Nambu bracket which produces the correct Hamiltonian time evolution. Existence and explicit forms of pairwise compatible multi-Hamiltonian structures for any maximal superintegrable system have been established. The Calogero–Moser system, motion of a charged particle in a uniform perpendicular magnetic field and Smorodinsky–Winternitz potentials are considered as illustrative applications and their symmetry algebras as well as their Nambu formulations and alternative Poisson structures are presented.

We study the quantum-mechanical evolution of the nonrelativistic oscillator, rapidly moving in the media with the random vector fields. We calculate the evolution of the level probability distribution as a function of time, and obtain rapid level diffusion over the energy levels. Our results imply a new mechanism of charmonium dissociation in QCD media.

We study the replacement of SU(3) by SU_q(3) in standard gauge theories. At the level of a global theory there is a physically sensible SU_q(3) formalism with measurable differences from the SU(3) theory.

The simplest spinor representations of the Poincaré group in flat ten and eleven dimensions with all possible signatures are considered. The possible superalgebraic extensions of the Poincaré algebra that are consistent with these spinor representations are provided, with the assumption that the only Bosonic operator that does not commute with the Fermionic operators is the generator of rotations. It is shown that the magnitude of the momentum is bounded above by the central charges, except when there is one time dimension, in which case the momentum is bounded below. An argument is made that this latter property is true in all dimensions.