Issue 1-2/2011

UDK 530.145
I. THE ISOTOPIC FOLDY-WOUTHUYSEN REPRESENTATION AND CHIRAL SYMMETRY / V. P. Neznamov // Р. 3
The paper introduces the isotopic Foldy-Wouthuysen representation. This representation was used to derive equations for massive interacting fermion fields.
When the interaction Hamiltonian commutes with the matrix γ⁵, these equations possess chiral invariance irrespective of whether fermions have mass or are massless.
The isotopic Foldy-Wouthuysen representation preserves the vector and axial currents irrespective of the fermion mass value. In the Dirac representation, the axial current is preserved only for massless fermions.
In the isotopic Foldy-Wouthuysen representation, the ground state of fermions (vacuum) turns out to be degenerate, and therefore there is the possibility of spontaneously breaking parity (P-symmetry).
This study considers the example of constructing a chirally symmetric quantum electrodynamics framework in the isotopic Foldy-Wouthuysen representation. A number of physical processes are calculated in the lowest orders of the perturbation theory. Final results of the calculations agree with the results of the standard quantum electrodynamics.

UDK 530.145
II. THE STANDARD MODEL IN THE ISOTOPIC FOLDY-WOUTHUYSEN REPRESENTATION WITHOUT HIGGS BOSONS IN THE FERMION SECTOR. SPONTANEOUS BREAKING OF PARITY AND «DARK MATTER» PROBLEMS / V. P. Neznamov // Р. 27
The Standard Model with massive fermions is formulated in the isotopic Foldy-Wouthuysen representation. SU(2)xU(1)-invariance of the theory in this representation is independent of whether fermions possess mass or not, and, consequently, it is not necessary to introduce interactions between Higgs bosons and fermions.
The study discusses a possible relation between spontaneous breaking of parity in the isotopic Foldy-Wouthuysen representation and the composition of elementary particles of «dark matter».

UDK 530.145; 514.764.2; 530.145.7
UNIQUENESS AND SELF-CONJUGACY OF DIRAC HAMILTONIANS IN ARBITRARY GRAVITATIONAL FIELDS / M. V. Gorbatenko, V. P. Neznamov // Р. 34
Proofs of two statements are provided in this paper. First, the authors prove that the formalism of the pseudo-Hermitian quantum mechanics allows the description of the Dirac particles motion in the terms of arbitrary stationary gravitational fields. Second, it is proved that using the Parker weight operator and the subsequent transition to the η-representation gives the transformation of the Schrödinger equation for nonstationary metric, when the evolution operator becomes self-conjugate. The scalar products in the η-representation are flat, which makes possible the use of a standard mechanism for the Hermitian quantum mechanics.
Based on the results of this paper the authors draw a conclusion about solution of the problem of uniqueness and self-conjugacy of Dirac Hamiltonians in arbitrary gravitational fields including those dependent on time.
The general approach is illustrated by the example of Dirac Hamiltonians for several stationary metrics, as well as for the spatially plane and the open Freedman models.

UDK 621.039.517
PROGRAM MURE VERIFICATION FOR THE CALCULATION OF DECAY HEAT OF THE DISCHARGE NUCLEAR FUEL / M. S. Onegin, I. V. Ryzhov // Р. 47
The verification of the program MURE for the calculation of the decay heat in the discharge fuel has been made. The calculated decay head was compared with the experimental one as for small samples of ^{235, 238}U and ²³⁹Pu and also for fuel assemblies of PWR reactors. The disagreement between calculations and experiment doesn’t exceed 15 % for decay time greater than 10 seconds.

UDK 530.145; 514.764; 530.145.7
ATOMS AND FORCES OF INTERACTION BETWEEN ELEMENTARY PARTICLES IN THE EXPANDING UNIVERSE / M. V. Gorbatenko, V. P. Neznamov // Р. 55
The earlier developed algorithm for constructing a self-conjugate Hamiltonian in the η-representation for Dirac particles interacting with a general gravitational field is extended to the case of electromagnetic fields. This Hamiltonian is applied to the case when the gravitational field describes the spatially flat Freedman model, and the electromagnetic field is the Coulomb potential extended to the case of this model.
The analysis of atomic systems and electromagnetic forces of interaction under the conditions of spatially flat expansion of the universe has demonstrated that the system of atomic levels does not change with cosmological time. On the contrary, the forces of interaction between elementary particles vary as the universe expands. Spectral lines of atoms in the spatially flat expanding universe are identical at different points of cosmological time. The results support the concepts of the standard cosmological model about the mechanism of redshift of atomic spectra.

UDK 539.17
INVARIANCE OF GENERAL NEUTRON TRANSPORT EQUATION IN SPECIFIC PROFILED SYSTEMS AND ITS IMPLICATIONS / N. B. Babichev, P. S. Bondarev, I. V. Lutikov, V. P. Neznamov // Р. 61
A special class of profiled system has been found for which general linear kinetic equation is invariant with respect to similarity transformations. On this basis, exact relationships between different physical quantities have been derived, on which neutron kinetics processes depend.

UDK 539.17
SOLUTION OF A ONE–VELOCITY EIGENVALUE AND EIGENFUNCTION PROBLEM IN NEUTRON KINETICS VALID FOR UNIFORM SINGLE–CONNECTED OBJECTS WITH NON–CONCAVE OUTER SURFACE / N. B. Babichev, I. V. Lutikov // Р. 65
Eigenvalue and Eigenfunction problem has been solved. The behavior of eigenvalue dependence on nuclear–physical properties of a substance has been determined. Physical meaning of specific neutron transport equations in uniform systems has been discussed.

UDK 539.17
SOLUTION OF GENERAL MILNE’S PROBLEM FOR TWO MEDIA, AT LEAST ONE MULTIPLYING NEUTRONS / P. S. Bondarev // Р. 70
Exact analytical solution has been found for the problem of spatial distribution of neutrons in a supercritical active system consisting of two semi-infinite media in contact through a plane interface.

UDK 533.9.01+533.951.2-3
NON-LINEAR THEORY OF ELECTROSTATIC WAVES IN DUSTY PLASMA / A. E. Dubinov, M. A. Sazonkin // Р. 77
Influence of a dust fraction on electrostatic wave propagation in dusty plasmas is studied in the paper. Cases of both negative and positive charge of the dust particles are considered, and the charge is considered to be constant. Analytical solutions of linear and non-linear equations of Langmuir, ion-acoustic and dust-acoustic waves are obtained. The non-linear equations are solved with the Sagdeev’s pseudopotential method. Areas of parameters, where periodic and solitary waves exist, are determined. New solution is found in the form of strongly non-linear ion-acoustic wave of high amplitude. Graphs of profiles of all wave types are drawn.

UDK 539. 3: 539.42
ABOUT EFFECT OF «THE DUSTING» IN THE CLUSTER DYNAMICS METHOD / V. N. Piskunov, D. V. Tsaplin, R. A. Veselov // Р. 98
The results of research of the dusting, arising at an appearance of a plane shock wave (SW) on a free smooth surface of the homogeneous sample, in calculations with use of the cluster dynamics method (CDM) are presented. The outputs of three-dimensional calculations show that within the limits of this model the dusting is caused not only the physical reasons, but also stray calculating effects. The one-dimensional model is developed for research of methodical questions on movement of clusters at the disturbance propagation. By means of this model the behaviour of frontier clusters caused by an appearance of SW is investigated. The nature of frontier clusters fluctuations are analysed, and the influence of an anharmonicity of interpartial potential is researched. It is shown, that the most high-frequency mode of fluctuations of a lattice of clusters (with movement of neighbors in an antiphase) plays the important role in stray dusting effects. This mode is caused anharmonic potential. Hence the criterion is produced, allowing to define the threshold loading speed at which the dusting arises in real three-dimensional problems. The method of elimination of calculating dusting effects is offered. This method is a modification of the equations of movement of clusters. Efficiency of the new equations is checked up in a series of three-dimensional calculations. Suggested approach completely eliminates stray dusting effects and preserves the basic physical laws of loading and following movement of the sample.