Volume 28, Issue 3, May 1997
28(1997); http://dx.doi.org/10.1134/1.953038View Description Hide Description
The problems associated with multiparticle production in model scalar theories are discussed. When the number of emitted particles is comparable to the inverse coupling constant, ordinary perturbation theory is inapplicable. The possibility of using semiclassical methods to calculate the multiparticle cross sections taking into account all important loop corrections is studied.
Lie groups and differential equations: symmetries, conservation laws, and exact solutions of mathematical models in physics28(1997); http://dx.doi.org/10.1134/1.953039View Description Hide Description
The basics of the modern group-theoretical analysis of differential equations are presented in a form suitable for beginners. This is the mathematical theory of symmetries and conservation laws, and the technique of using them to obtain exact solutions of mathematical models based on (nonlinear) differential equations (both ordinary and partial). The group analysis naturally reveals the variables most suitable for a given problem and the related differential-geometrical structures such as the (pseudo)-Riemannian geometry, the connections, and the Hamiltonian and Lagrangian formalisms. The range of possible applications includes the mechanics of continuous media (gas- and hydrodynamics, nonlinear elasticity and plasticity theory of solids), nonlinear acoustics, magnetic hydrodynamics, the theory of gravitation and other nonlinear field theories (gauge and chiral fields, string theories, and so on), chemistry (chromatography and electrophoresis), and biology. Promising applications to linear theories like quantum mechanics—the construction of new exact solutions, the theory of separation of variables, and so on—are also discussed.
28(1997); http://dx.doi.org/10.1134/1.953040View Description Hide Description
New symmetries (quantum symmetries) formulated in the language of quantum groups are being used more and more in theoretical and mathematical physics. The present paper is devoted to a discussion of bicovariant differential calculus on quantum groups and quantum vector spaces, and is a sequel to a review published in this journal in 1995. A detailed exposition is given of the bicovariant theory of Woronowicz, which is now regarded as the basis for constructing the noncommutative differential geometry on quantum groups. The -matrix approach is used to give a complete description of the differential calculus on the group and on linear quantum spaces. It is shown how the differential algebra on the group can be obtained (as a subalgebra) from the differential algebra on The problems of the bicovariant differential calculus on the groups and are discussed. Essential supplementary information on the general theory of quantum groups, not covered in the first part of the review, is also given.
28(1997); http://dx.doi.org/10.1134/1.953041View Description Hide Description
The most important results from the last thirty years of the study of matter using muons at the 680-MeV proton accelerator (phasotron) at the JINR Laboratory of Nuclear Problems are reviewed. The muon technique, which has become known as the μSR method, was first widely used by a group of investigators from the Laboratory of Nuclear Problems, the Kurchatov Institute, and the Institute of Theoretical and Experimental Physics. The principles of the μSR method are described, along with the experimental conditions under which these studies are performed at the phasotron. The results of the experimental measurement of the asymmetry coefficient in decay are discussed, along with results of the experiments which led to the discovery of two-frequency muonium spin precession, the sub-barrier incoherent diffusion of a positively charged muon in metals, and muonium in solids. The most important results on the study of semiconductors,dielectrics, ferro- and antiferromagnets,high-temperature superconductors, the diffusion of positively charged muons in metals, and chemical reactions involving muonium are presented, and the use of negatively charged muons to study matter is discussed.