International Journal of Modern Physics A

In this work, I study the propagation of cosmic rays inside the magnetic field of the earth, at distances d≤500 km from its surface; at these distances, the geomagnetic field deeply influences the diffusion motion of the particles.

I compare the different effects of the interplanetary and of the geomagnetic fields, by also discussing their role in the cosmic rays transport equation; then, I present an analytical method to solve such an equation through a factorization technique. In this way, it is possible to reduce the initial second-order, partial derivatives differential equation into a more simple, Riccati-like equation, which, finally, can be solved by using standard Runge–Kutta–Merson routines.

The results here obtained may have some interest in view of the future AMS (Alpha Magnetic Spectrometer) data, which will be collected at an altitude of about 400 km above the earth surface. Moreover, the study of the propagation of particles having different charges and masses may also help in testing the presence of antimatter and antinuclei in cosmic rays; some theoretical implications of this possibility will also be discussed in the light of the perspectives opened by the AMS Experiment.

This work consists of two interrelated parts. First, we derive massive gauge-invariant generalizations of geometric actions on coadjoint orbits of arbitrary (infinite-dimensional) groups G with central extensions, with gauge group H being certain (infinite-dimensional) subgroup of G. We show that there exist generalized "zero-curvature" representations of the pertinent equations of motion on the coadjoint orbit. Second, in the special case of G being the Kac–Moody group, the equations of motion of the underlying gauged WZNW geometric action are identified as additional-symmetry flows of generalized Drinfeld–Sokolov integrable hierarchies based on the loop algebra . For the latter hierarchies are equivalent to the class cKP_R,M of constrained (reduced) KP hierarchies. We describe in some detail the loop algebras of additional (nonisospectral) symmetries of cKP_R,M hierarchies. Apart from gauged WZNW models, certain higher-dimensional nonlinear systems such as Davey–Stewartson and N-wave resonant systems are also identified as additional symmetry flows of cKP_R,M hierarchies. Also we present the explicit derivation of the general Darboux–Bäcklund solutions of cKP_R,M hierarchies preserving their additional (nonisospectral) symmetries, which for R=1 contain among themselves solutions to the gauged SL(M+1)/U(1)×SL(M) WZNW field equations.

Using a one-loop renormalization group improvement for the effective potential in the Higgs model of electrodynamics with electrically and magnetically charged scalar fields, we argue for the existence of a triple (critical) point in the phase diagram (), where λ_run is the renormalized running self-interaction constant of the Higgs scalar monopoles and g_run is their running magnetic charge. This triple point is a boundary point of three first-order phase transitions in the dual sector of the Higgs scalar electrodynamics: The "Coulomb" and two confinement phases meet together at this critical point. Considering the arguments for the one-loop approximation validity in the region of parameters around the triple point A we have obtained the following triple point values of the running couplings: , which are independent of the electric charge influence and two-loop corrections to with high accuracy of deviations. At the triple point the mass of monopoles is equal to zero. The corresponding critical value of the electric fine structure constant turns out to be by the Dirac relation. This value is close to the , which in a U(1) lattice gauge theory corresponds to the phase transition between the "Coulomb" and confinement phases. In our theory for α ≥ α_crit there are two phases for the confinement of the electrically charged particles. The results of the present paper are very encouraging for the antigrand unification theory which was developed previously as a realistic alternative to SUSY GUT's. The paper is also devoted to the discussion of this problem.

We study the Hamilton–Jacobi quantization of supersymmetric quantum mechanics. The equations of motion of the Grassmann variables are obtained from the integrability conditions. The results are in agreement with those obtained by Dirac's procedure.

We consider proton decay in theories that contain large extra dimensions. If virtual black hole states are allowed by the theory, as is generally the case, then proton decay can proceed via virtual black holes. The experimental limits on the proton lifetime place strong constraints on the quantum gravity scale M_qg (the effective Planck mass). For most theories, this implies a lower bound of M_qg>10¹⁶ GeV. The corresponding bound on the size of large extra dimensions is ℓ<10^6/n×10^-30 cm, where n is the number of such dimensions. Regrettably, for most theories this limit rules out the possibility of observing large extra dimensions at accelerators or in millimeter scale gravity experiments. Conversely, proton decay could be dominated by virtual black holes, providing an experimental probe to study stringy quantum gravity physics.

We show that the truncation of twisted Yangians are isomorphic to finite -algebras based on orthogonal or symplectic algebras. This isomorphism allows us to classify all the finite-dimensional irreducible representations of the quoted -algebras. We also give an R matrix for these -algebras, and determine their center.

We study the effect of a strong magnetic field on interacting quark matter and apply the same to strange star. We find that interacting strange matter is less stable than noninteracting strange matter in the presence of a strong magnetic field. We then calculate strange star structure parameters such as mass and radius and find that the strange star is less compact for interacting quark matter than for free quark matter in presence of strong magnetic field. The maximum masses of strange stars are found to be within the recent observational limit.