Modified Gibbs's representation of rotation matrix

A modified Gibbs's rotation matrix is derived and the connection with the Euler angles, quaternions, and Cayley$-$Klein parameters is established. As particular cases, the Rodrigues and Gibbs parameterizations of the rotation are obtained. The composition law of two rotations from the quaternion representation is presented showing a convenient expression for calculating the successive rotations.Comment: 17 page

Effective Lagrangian and Dynamical Symmetry Breaking in the SU(2)XU(1) NJL Model

Dynamical symmetry breaking and the formation of scalar condensates in the SU(2)XU(1) Nambu-Jona-Lasinio model with two coupling constants has been studied in the framework of the mean field approximation. The bosonization procedures of the model are performed using the functional integration method. The possibility of the spontaneous CP symmetry breaking in the model under consideration has been shown. The mass spectrum of the bound states of fermions, as well as the effective Lagrangian of interacting scalar and pseudoscalar mesons are obtained.Comment: 7 pages, LaTeX. Minor correction

Kalb-Ramond fields in the Petiau-Duffin-Kemmer formalism and scale invariance

Kalb-Ramond equations for massive and massless particles are considered in the framework of the Petiau-Duffin-Kemmer formalism. We obtain $10\times10$ matrices of the relativistic wave equation of the first-order and solutions in the form of density matrix. The canonical and Belinfante energy-momentum tensors are found. We investigate the scale invariance and obtain the conserved dilatation current. It was demonstrated that the conformal symmetry is broken even for massless fields.Comment: 9 pages, no figure

Maxwell - Chern - Simons topologically massive gauge fields in the first-order formalism

We find the canonical and Belinfante energy-momentum tensors and their nonzero traces. We note that the dilatation symmetry is broken and the divergence of the dilatation current is proportional to the topological mass of the gauge field. It was demonstrated that the gauge field possesses the `scale dimensionality' d=1/2. Maxwell - Chern - Simons topologically massive gauge field theory in 2+1 dimensions is formulated in the first-order formalism. It is shown that 6x6-matrices of the relativistic wave equation obey the Duffin - Kemmer - Petiau algebra. The Hermitianizing matrix of the relativistic wave equation is given. The projection operators extracting solutions of field equations for states with definite energy-momentum and spin are obtained. The 5x5-matrix Schrodinger form of the equation is derived after the exclusion of non-dynamical components, and the quantum-mechanical Hamiltonian is obtained. Projection operators extracting physical states in the Schrodinger picture are found.Comment: 18 pages, correction in Ref. [5

Stabilization of a light bullet in a layered Kerr medium with sign-changing nonlinearity

Using the numerical solution of the nonlinear Schr\"odinger equation and a variational method it is shown that (3+1)-dimensional spatiotemporal optical solitons, known as light bullets, can be stabilized in a layered Kerr medium with sign-changing nonlinearity along the propagation direction.Comment: 4 pages, 3 PS figure

Solutions of Podolsky's Electrodynamics Equation in the First-Order Formalism

The Podolsky generalized electrodynamics with higher derivatives is formulated in the first-order formalism. The first-order relativistic wave equation in the 20-dimensional matrix form is derived. We prove that the matrices of the equation obey the Petiau-Duffin-Kemmer algebra. The Hermitianizing matrix and Lagrangian in the first-order formalism are given. The projection operators extracting solutions of field equations for states with definite energy-momentum and spin projections are obtained, and we find the density matrix for the massive state. The $13\times 13$-matrix Schrodinger form of the equation is derived, and the Hamiltonian is obtained. Projection operators extracting the physical eigenvalues of the Hamiltonian are found.Comment: 17 pages, minor corrections, published versio

On Possible Light-Torsion Mixing in Background Magnetic Field

The interaction of the light with propagating axial torsion fields in the presence of an external magnetic field has been investigated. Axial torsion fields appearing in higher derivative quantum gravity possess two states, with spin one and zero, with different masses. The torsion field with spin-0 state is a ghost that can be removed if its mass is infinite. We investigate the possibility when the light mixes with the torsion fields resulting in the effect of vacuum birefringence and dichroism. The expressions for ellipticity and the rotation of light polarization axis depending on the coupling constant and the external magnetic field have been obtained.Comment: 12 pages, title changed, shortened journal version, accepted in Eur.Phys.J.

Comparative analysis of order allocation methods and intelligent systems for effective download of production capacities of manufacturing enterprise

The article compares the planning systems of the enterprise, determines their opportunities to use simulation for the process of distribution of production orders. A comparative review of the methods used in production planning systems and the multi-agent approach in solving the problem of the allocation of production orders is carried out. The possibility of approaches in cases when it is impossible to perform production tasks within the established time frame is considered, as well as to effectively load the available capacities of the units. In case it is not possible to produce the necessary quantity to distribute the part to another, similar to the type of equipment used, but different from it by the quantity and production capacity of the unit. Transmission must be carried out under the condition of sufficient capacity in the subdivision. The results of theoretical and experimental studies are presented. In the process of work, we used the BPsim. MAS dynamic modeling system. An automated system with the possibility of using simulation for the allocation of production orders is considered. © 2019 IOP Publishing Ltd. All rights reserved.The work was supported by Act 211 Government of the Russian Federation, contract № 02.A03.21.0006