A simple variational principle for classical spinning particle with anomalous magnetic momentum

We obtain Bargmann-Michel-Telegdi equations of motion of classical spinning particle using Lagrangian variational principle with Grassmann variables.Comment: 3 pages, late

Massless fields over R1×H3R^1 \times H^3 space-time and coherent states for the Lorentz group

The solutions of the arbitrary-spin massless wave equations over ${\bf R}^1 \times H^3$ space are obtained using the generalized coherent states for the Lorentz group. The use of these solutions for the construction of invariant propagators of quantized massless fields with an arbitrary spin over the ${\bf R}^1 \times H^3$ space is considered. The expression for the scalar propagator is obtained in the explicit form.Comment: 6 pages, LATEX, no figures. To appear in Modern Phys. Lett.

Coherent states for the hydrogen atom

We construct a system of coherent states for the hydrogen atom that is expressed in terms of elementary functions. Unlike to the previous attempts in this direction, this system possesses the properties equivalent to the most of those for the harmonic oscillator, with modifications due to the character of the problem.Comment: 6 pages, LATEX, using ioplppt.sty and iopfts.sty. v.2: some misprints are corrected. To appear in J.Phys.

Coherent states for the hydrogen atom: discrete and continuous spectra

We construct the systems of generalised coherent states for the discrete and continuous spectra of the hydrogen atom. These systems are expressed in elementary functions and are invariant under the $SO(3, 2)$ (discrete spectrum) and $SO(4, 1)$ (continuous spectrum) subgroups of the dynamical symmetry group $SO(4, 2)$ of the hydrogen atom. Both systems of coherent states are particular cases of the kernel of integral operator which interwines irreducible representations of the $SO(4, 2)$ group.Comment: 15 pages, LATEX, minor sign corrections, to appear in J.Phys.

Poisson bracket in classical field theory as a derived bracket

We construct a Leibniz bracket on the space $\Omega^\bullet (J^k (\pi))$ of all differential forms over the finite-dimensional jet bundle $J^k (\pi)$. As an example, we write Maxwell equations with sources in the covariant finite-dimensional hamiltonian form.Comment: 4 page

Quantization of fields over de Sitter space by the method of generalized coherent states

A system of generalized coherent states for the de Sitter group obeying the Klein-Gordon equation and corresponding to the massive spin zero particles over the de Sitter space is considered. This allows us to construct the quantized scalar field by the resolution over these coherent states; the corresponding propagator is computed by the method of analytic continuation to the complex de Sitter space and coincides with expressions obtained previously by other methods. Considering the case of spin 1/2 we establish the connection of the invariant Dirac equation over the de Sitter space with irreducible representations of the de Sitter group. The set of solutions of this equation is obtained in the form of the product of two different systems of generalized coherent states for the de Sitter group. Using these solutions the quantized Dirac field over de Sitter space is constructed and its propagator is found. It is a result of action of some de Sitter invariant spinor operator onto the spin zero propagator with an imaginary shift of a mass. We show that the constructed propagators possess the de Sitter-invariance and causality properties.Comment: 19 pages, LATEX, using ioplppt.sty and iopfts.st

INVESTIGATION OF THE EFFICIENCY OF CONFORMAL COOLING CHANNELS OF COMPOSITE MOLDS

The article deals with the issue of evaluating the performance of a composite metal-metal-polymer mold. The use of a composite mold, including a forming plate consisting of a metal, and a metal polymer introduced with a low cooling efficiency of such a mold. For this reason, it is important to develop technological solutions that ensure the efficient operation of the cooling system. The article provides mathematical calculations of the required amount of heat flow when molding thermoplastics into a mold. Further, based on the calculated data, a study is made using finite elements of the thermal conductivity of the metal-polymer part. The design of the composite forming plate of the mold described in the article involves the manufacture of a cooling channel profile as close as possible to the forming part of the mold and located in the metal-polymer part. Based on the analysis of the temperature viscosity of the metal-polymer part of the mold, conclusions and recommendations are given for the design of a curved investment mold. It allows designers to calculate the optimal geometric parameters of the cooling system. The design and manufacture of conformal cooling stages in the metal-polymer part is likely to be preferable for cooling the forming part of the mold by bringing the cooling reversal surface closer to the surface of the forming mold, resulting in increased durability and productivity of the composite mold.</jats:p