Quantization of bosonic fields with two mass and spin states

We investigate bosonic fields possessing two mass and spin states. The density matrix in the first order formalism is obtained. The quantization of fields in the first order formulation is performed and propagators are found.Comment: 9 page

"Square Root" of the Proca Equation: Spin-3/2 Field Equation

New equations describing particles with spin 3/2 are derived. The non-local equation with the unique mass can be considered as "square root" of the Proca equation in the same sense as the Dirac equation is related to the Klein-Gordon-Fock equation. The local equation describes spin 3/2 particles with three mass states. The equations considered involve fields with spin-3/2 and spin-1/2, i.e. multi-spin 1/2, 3/2. The projection operators extracting states with definite energy, spin, and spin projections are obtained. All independent solutions of the local equation are expressed through projection matrices. The first order relativistic wave equation in the 20-dimensional matrix form, the relativistically invariant bilinear form and the corresponding Lagrangian are given. Two parameters characterizing non-minimal electromagnetic interactions of fermions are introduced, and the quantum-mechanical Hamiltonian is found. It is proved that there is only causal propagation of waves in the approach considered.Comment: 17 pages, corrections in Eqs. (50), (51

Field theory of massive and massless vector particles in the Duffin - Kemmer - Petiau formalism

Field theory of massive and massless vector particles is considered in the first-order formalism. The Hamiltonian form of equations is obtained after the exclusion of non-dynamical components. We obtain the canonical and symmetrical Belinfante energy-momentum tensors and their nonzero traces. We note that the dilatation symmetry is broken in the massive case but in the massless case the modified dilatation current is conserved. The canonical quantization is performed and the propagator of the massive fields is found in the Duffin - Kemmer - Petiau formalism.Comment: 20 pages, typos corrected, a reference added, journal version, accepted in Int.J.Mod.Phys.

A way to estimate the discharge of the melt jet flowing out of a melting furnace

A way to estimate the discharge of melt jet flowing out of a melting furnace is examined. We analyze the efficiency of algorithms for image matching in order to estimate the jet velocity. To decrease the time needed for estimating the 2D motion of melt flow, it is suggested to calculate the shift of 2D images according to two independent 1D projections. This approach makes it possible to estimate on-line the flow rate and to do it in television standard. © 2013 Pleiades Publishing, Ltd

Implementation of Information Technologies in Forest Industry

The article is devoted to the development and implementation of manufacturing execution system (MES) for forest enterprises in context of automatic generation of the primary data about logistics processes of roundwood. The system enables on-line workflow monitoring at the low landing as well as round wood acceptance and shipment on line monitoring. The automation of this process is achieved through the use of specific software for mobile roundwood measurement based on photogrammetry. It implicates the usage of automatic processing and analysis for the images of logs’ abuts. The main advantage of MES is its complete integration with the given software

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

The unsupervised learning algorithm for detecting ellipsoid objects

This paper is devoted to the analysis and implementation of the algorithms for automatic detection of the circular objects in the image. The practical aim of this task is development of the algorithm for automatic detection of log abuts in the images of roundwood batches. Based on literature review four methods were chosen for the further analysis and the best performance out of them was provided by ELSD algorithm. Some modifications were implemented to the algorithm to fulfill the requirements of the given task. After all, the modified ELSD algorithm was tested on the dataset of the images. The relative accuracy of the algorithm in comparison with manual measurement is 95.2% for the images with total area of background scene less than 20%. © 2019 International Association of Computer Science and Information Technology

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

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