Table of contents

The status of string theory is reviewed, and major recent developments — especially those in going beyond perturbation theory in the string theory and quantum field theory frameworks — are analyzed. This analysis helps better understand the role and place of string theory in the modern picture of the physical world. Even though quantum field theory describes a wide range of experimental phenomena, it is emphasized that there are some insurmountable problems inherent in it — notably the impossibility to formulate the quantum theory of gravity on its basis — which prevent it from being a fundamental physical theory of the world of microscopic distances. It is this task, the creation of such a theory, which string theory, currently far from completion, is expected to solve. In spite of its somewhat vague current form, string theory has already led to a number of serious results and greatly contributed to progress in the understanding of quantum field theory. It is these developments which are our concern in this review.

Under conditions which are usually associated with collisionless plasma, and in which the mean free path of charged particles considerably exceeds the characteristic size of the spatial inhomogeneities involved, plasmas always contain slow particles whose mean free path proportional to the fourth power of their velocity is less than the inhomogeneity scale. Although relatively few in number, these subthermal particles play a dominant role in such 'weakly collisional' plasmas. In this paper, the results of the analytical kinetic theory of plasma are discussed, which highlight the determining role slow collisional particles play in such plasma phenomena as ion-acoustic wave damping and nonlinear electron-density perturbations due to the inhomogeneous intensity of the plasma-heating electromagnetic field. It is shown that by affecting these plasma properties the subthermal electrons correspondingly make an impact on parametric instabilities such as plasma radiation filamentation and stimulated Mandelstam– Brillouin scattering. Theoretical predictions are compared with numerical solutions of the Boltzmann equation. The concept of nonlocal plasma transfer processes, attracted to the interpretation of such solutions, is also discussed.

Attempts of designing economics along the lines of natural sciences (in particular, physics) with the use of mathematical modeling are reviewed. This area of research has come to be known as physical economics. Some topical questions of market economics are discussed; specifically, whether the market equilibrium is unique, whether transitions between stationary states are possible, and, if so, how these transitions proceed. By analogy with physics, the apparatus of mathematical modeling is widely used in answering these questions. It is shown that, under given external conditions, a self-sufficient country can be in two stationary, stable states — either in a high-productivity (HP) or in a low-productivity (LP) state. Transitions between them appear to be either an 'economical crisis' or an 'economical miracle'. It is shown that, for contemporary Russia, the crisis is already over, and the country is now in a stable LP state. Possible transitions to a HP state are discussed. The distributions of social elements over liquid accumulations and incomes are considered. It is shown that, in present-day Russia, these distributions are bimodal, meaning the coexistence of the poor and the wealthy with virtually no middle layer in between. In the tail of the distribution, a very small number of very wealthy people are present.