Quaternions and Small Lorentz Groups in Noncommutative Electrodynamics

Non-linear electrodynamics arising in the frames of field theories in noncommutative space-time is examined on the base of quaternion formalism. The problem of form-invariance of the corresponding nonlinear constitutive relations governed by six noncommutativity parameters $\theta_{kl}$ or quaternion \underline{K} = \underline{\theta} - i \underline{\epsilon} is explored in detail. Two Abelian 2-parametric small groups, SO(2) \otimes O(1.1) or T_{2}, depending on invariant length \underline{K}^{2}\neq 0 or \underline{K}^{2}= 0 respectively, have been found. The way to interpret both small groups in physical terms consists in factorizing corresponding Lorentz transformations into Euclidean rotations and Lorentzian boosts. In the context of general study of various dual symmetries in noncommutative field theory, it is demonstrated explicitly that the nonlinear constitutive equations under consideration are not invariant under continuous dual rotations, instead only invariance under discrete dual transformation exists.Comment: 8 page

Radiative tail from the quasielastic peak in deep inelastic scattering of polarized leptons off polarized He-3

The contribution of the radiative tail from the quasielastic peak to low order radiative correction to deep inelastic scattering of polarized leptons by polarized $^3$He was calculated within the sum rules formalism and $y$-scaling hypothesis. Numerical analysis was carried out under the conditions of HERMES experiment.Comment: 10 pages, 3 figure

Multi-center MICZ-Kepler system, supersymmetry and integrability

We propose the general scheme of incorporation of the Dirac monopoles into mechanical systems on the three-dimensional conformal flat space. We found that any system (without monopoles) admitting the separation of variables in the elliptic or parabolic coordinates can be extended to the integrable system with the Dirac monopoles located at the foci of the corresponding coordinate systems. Particular cases of this class of system are the two-center MICZ-Kepler system in the Euclidean space, the limiting case when one of the background dyons is located at the infinity as well as the model of particle in parabolic quantum dot in the presence of parallel constant uniform electric and magnetic fields.Comment: 5 pages, revtex, revised versio

Computational modelling of mil composites fracture under dynamic loading

The processes of multilayer composites failure under dynamic loading were investigated