The important role of functional integrals in modern physics

Jean Zinn‐Justin

Прохоров Лев Васильевич, Sergei V. Shabanov

Introduction Preliminary remarks The path integral formalism is one of the most important tools in modern theoretical physics. Integration in functional spaces was considered for the first time by Norbert Wiener in his studies of diffusion processes [60, 61]. The corresponding integration measure is now known as the Wiener measure, i.e. the so-called Gaussian path integrals were studied. In quantum mechanics, functional integrals were introduced by R. Feynmann [62, 63] who was inspired by important observations due to P. A. M. Dirac concerning a relation between wave function and classical action [64, 65]. In modern physics the path integral formalism is applied not only to developing a quantum description for systems with infinitely many degrees of freedom as, for example, in quantum field theories or condensed matter physics, but also to ordinary quantum mechanical problems. Moreover there is a tendency to reformulate standard quantum mechanical problems (such as a particle in a “box” or potential well [66, 67], or a particle in the Coulomb field [68]) within the framework of the path integral method. The reason for doing this is rather obvious: physicists develop a new mathematical tool, a new language and, in order to comprehend all of its subtleties, it is necessary to investigate as many concrete examples as possible. Use of the path integral formalism is widespread in quantum field theory because it is the most adequate mathematical tool for a wide range of problems which allows, not only for elegant formulation of problems, but also for a great deal of simplification of their theoretical analysis.

Viktor Nikolayevich Popov

Li-Man Tian, Yong-Li Wen, Yunfei Wang +5 more

The propagator plays a central role in path integral theory and therefore has significant value in various fields of modern quantum physics, where path integral representations can be used. However, owing to the fact that it has not been directly measured in experiment, progress of experimental studies of quantum systems based on path integral representations has been seriously limited. Recently, we proposed a propagator measurement scheme based on the direct measurement of the wave function and successfully performed the first experimental measurement of the propagator by using a single photon experiment. Furthermore, in this study, the quantum principle of least action is demonstrated for the first time. This research successfully addresses the technical challenges of path integral experimental studies. In this work, we review the research progress in this field, including a brief introduction to the basic concepts and research progress of direct wave function measurement, and a detailed description of the theoretical model, experimental design, and experimental results of propagator measurement. Finally, we introduce an important application example, which can serve as the experimental demonstration of the quantum principle of least action through propagator measurement. The research progress of propagator measurement reviewed in this work will provide important references for future experimental studies by using this method.

D. I. Blokhint︠s︡ev, B M Barbashov

Ревунов Сергей Евгеньевич, С. В. Кузнецов, O. A. Barkhatova +1 more

Introduction: the study considers the problem of observer’s status during specific quantum-mechanical experiments, in which the empirical result directly depends on the participation of the experimenter's mind. Here the problem arises of the connection between the mind of the observer and the quantum-mechanical description of physical reality. The paper pays attention to modern trends in physics and philosophy devoted to the study of this phenomenon. Some aspects of the philosophical interpretation of the mind as a quantum mechanism are presented. Materials and Methods: the research materials demonstrate an overview of several common quantum-philosophical theories. Attempts have been made to search for the connection of quantum phenomena with the mechanisms of the functioning of human mind. The experimental background of quantum physics is demonstrated, providing material for analyzing the possibility of applying modern quantum theory to the question of identifying the relationship of the quantum approach and describing the problem of the influence of the observer’s mind on the result of a physical experiment. Results: the concept of quantum mechanics, taking into account the latest achievements and results of physics, philosophy and psychology, allows us to consider the mind of the observer as an integral part of the mechanism responsible for the formation of the surrounding physical reality. The anthropic principle of participation considered in the work gives the observer's mind a special role allowing to form a quantum-mechanical description of physical reality. Discussion and conclusions: it is shown that the mind of the observer plays an important role in quantum theory. Moreover, mind as a psychic phenomenon may be in fact identical with the quantum-mechanical concept of choosing an alternative. Given the fact that the brain's thought processes influence the measurement results, it can be assumed that mind changes quantum probabilities. This assumption allows us to take a different look at the concept of reality itself.