566 research outputs found
Modified Gibbs's representation of rotation matrix
A modified Gibbs's rotation matrix is derived and the connection with the
Euler angles, quaternions, and CayleyKlein 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
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 -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
Spectrometric characteristics of the total absorption cerenkov counter within the nanosecond time region
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.
Method for loading cargo trucks using two-dimensional packing algorithms
The paper describes the method for optimization of loading cargo trucks using two-dimensional packing algorithms. The point of this method is to reduce loading cargo problem to two-dimensional packing problem. This problem can be solved by using of various algorithms. There is analysis of several algorithms that are most often used in practical calculations of objects distribution in 2D space in this paper. The object of this study is transport of the metal processing company and its products (cargo). PHP programming language, MySQL database, and Apache web server are used to create client application. The interface developed using HTML5, CSS and javascript. © 2019 IOP Publishing Ltd. All rights reserved.The work was supported by Act 211 Government of the Russian Federation, contract № 02.A03.21.0006
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