Table of contents

We discuss the scale and chiral anomalies in quantum chromodynamics and their implications for the theory of hadrons. In the first part the physical meaning of the anomaly is demonstrated. To this end the simplest gauge model is considered—two-dimensional Schwinger model. In this model it is extremely easy to explain what properties of the theory are responsible for the quantum anomaly and the physical nature of the phenomenon is elucidated. The second part is devoted to derivation of the anomaly relations within QCD. The subtle question of the multiloop corrections is discussed. The third part presents applications. Starting from the chiral and scale anomalies we obtain low-energy theorems which lead, in turn, to predictions for observable processes. In particular, a proof based on first principles is given of the existence of massless pions, the amplitudes are calculated for the conversion of gluon operators into pions which can be measured experimentally. Other practical problems are also considered, the solution of which turns out to be possible due to anomalies.

The current state of the Lin-Shu density wave theory is discussed in the light of modern observational data. Much attention is paid to the problem of wave excitation and to the response of the interstellar gas to the wave gravitational potential. It is noted that the major predictions of the density wave theory—the galactic shock waves, the spiral velocity field of stars, and the age gradient across the spiral arms—have become fundamental observational facts at present, so that the density wave theory now has no competition from alternative theories. The nature of flocculent spirals is also discussed since, unlike regular spirals, they are probably not connected with density waves but with the effects of induced star formation in differentially rotating galactic disks.

Theoretical and experimental studies of the interaction between atoms and molecules chemisorbed on the surface of a metal are described. The basic interaction mechanisms are studied theoretically: 1) direct—owing to the direct exchange of electrons between adatoms; 2) indirect—owing to the exchange of electrons through the conduction band of the metal substrate; and, 3) electrostatic—owing to the exchange of photons and surface plasmons between charged adatoms. Experimental studies performed with a field-ion microscope and by the LEED technique are described in detail. The two-dimensional adatom structures observed on the channeled faces of transition metals enable studying the interaction at record large distances (up to 25 Å). The following are studied briefly: the interaction of adatoms on a semiconductor surface, interaction-induced restructuring in an adsorbed atomic film, reconstruction of clean metal and semiconductor surfaces, and other manifestations of interaction in adsorption systems.

A review of current research in optoacoustics. The authors describe and examine several new developments in the field: guided transport of sound in the wake of a light beam; new techniques of detecting objects in transparent and turbid media; high-resolution nonlinear subsurface imaging using self-focused beams and guided transport of the response signal; control of the spectrum and amplitude of a thermoacoustic pulse due to cropping of the light beam cross-section, lateral contact with an interface, semi-submerged light beam, and so forth. Enhancement of acoustic transmissivity by means of a laser beam is examined. The authors indicate the practical applications of these new developments.

Temporal polarization instability is seen as an oscillatory or random variation in time of the polarization parameters of light interacting with a nonlinear system. Spatial polarization instability is the formation of "frozen" complex quasiperiodic or pseudochaotic distributions of the polarization parameters of a wave along the direction of propagation. The problem of polarization instability or multistability is intimately related to the polarization of eigenwaves in the nonlinear problem and their transformation as a result of "hard" and "soft" spontaneous polarization symmetry breaking. This paper presents a review of publications on polarization instabilities in passive nonlinear optical systems, including Fabry–Perot resonators, gyrotropic media, systems with strong two-photon absorption, birefringent crystals, fiber lightguides, and isotropic media.