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Methods are suggested for studying the structure of particles. The nuclear structure, the electromagnetic structure, and the effects of nucleons on nuclear structure are analyzed. An analysis and critical remarks are presented on Hofstadter experiments, and an attempt is made to interpret the electromagnetic structure of central nucleon areas. The optical nucleon model is also discussed. 60 references. (R.V.J.)

In this article a critical analysis is given of basic geometric concepts as applied to the physics of the microcosmos. The article begins with an outline of geometry in macroscopic physics. This part is based on the classical papers of H. Poincare, A. Einstein, and A. A. Fridman. An indication of possible limitations on the concept of a point event associated with limiting densities of matter represents new material. Subsequently localization of elementary particles is discussed and limits of possible accuracy are indicated. In the article it is emphasized that the logical structure of local quantum field theory presupposes the existence of particles of arbitrarily large mass. The existence of "maximons"–particles of a limiting, but finite mass–strong gravitation (collapse of particles), instability of particles with respect to decay due to the weak interaction (this interaction can become strong for very heavy particles and can lead to lead to total instability of such a particle). In the conclusion of the article two features of a nonlocal field theory are considered. In this theory the coordinates of a point event are operators, while momentum space remains a numerical space (either curved or flat). The first variant presupposes commutation conditions for the coordinates of a point (the Snyder-Kadyshevskii theory), while the second variant presupposes anticommutation conditions (the author's theory).

Physicists are becoming more interested in solving the equations of quantum theory without using methods requiring expansion in powers of the interaction constant. The perturbation-theory method, which gave results that agree splendidly with experiment in quantum electrodynamics, turned to be inapplicable in strong-interaction theory. One of the methods in which a radical attempt is made to go beyond the framework of perturbation theory, is the method of functional integration in quantum theory, first proposed by Feynman. The present review, which is devoted to this method, introduces in lucid fashion the concepts of functional integrations and then explains some applications of this method in quantum field theory. Much attention is paid to the use of functional integrals in infrared and high-energy asymptotic relations in field theory. The review does not claim an exposition of the mathematical difficulties connected with the concept of functional integral, and focuses attention to certain successes in its use in quantum physics.

In the firsc part of the article (chapter 2) a brief review is given of the characteristics of existing and projected accelerators. The second part (chapter 3) is devoted to enumeration of the main problems of elementary-particle physics whose solution depends substantially on the maximum energy achievable in the center-of-mass system: a) the search for an elementary length, i.e., a hypothetical dimensional quantity which provides an energy scale at ultrahigh energies, b) The search for quarks, Schwinger dyons, and other unusual particles, c) The study of self-similar behavior in lepton-hadron and hadron-hadron collisions, particularly the search for deviations from self-similarity which would indicate the appearance of a new energy scale in high-energy physics, d) Further precision experiments in lepton physics in which deviations from the predictions of quantum electrodynamics at ultrasmall distances could be observed, e) The study of weak and weak-electromagnetic processes at high energies. In conclusion a discussion is given of the desirability of constructing a complex of colliding beams of protons, antiprotons, electrons, and positrons with a center-of-mass energy greater than 300 BeV.