Review of the Latest Theories of Nucleon Interactions*

Recently, a whole series of monographs and reviews have appeared, published by various publishing houses and devoted to questions of the theory of nucleon interactions. Among them, the review belonging to the well-known Swiss theoretical physicist G. Wentzel (Zurich) deserves attention. In this short review, a critical analysis and comparison is carried out

* G. Wentzel, Recent Research in Mesontheory, Rev. Mod. Phys., 19, 1 (1947).

various existing theories of the interaction of nucleons by means of the meson field.

The author first of all notes the possibility of introducing the concept of an elementary quantum particle (the meson), by means of which the nuclear interaction is effected, and, in particular, emphasizes the arguments underlying Yukawa’s theory, which say that the range of action of nuclear forces corresponds to the Compton wavelength of the particles introduced. The introduction of the concept of mesons is directly connected with the introduction of the concept of the probabilities of elementary quantum transitions of the field and of the nucleon system from one state to another, these transitions having a more elementary character than the concept of the meson. The task of the theory is to find principles and computational methods that could be used to obtain a complete picture of the experimental data.

Existing theories are divided into several groups, namely as follows:

I. Theories using the quantum-mechanical method of perturbation theory (expansion of the energy values of the closed states of the system in powers of the constant characterizing the interaction). Here we have before us all those theories which do not satisfy the requirements of relativistic invariance and which introduce the concept of the noncovariant density of the sources of the meson field. We must distinguish, depending on the character of the expansion, theories using an expansion in increasing powers of the constant, and theories using an expansion in decreasing powers of the constant (theories of weak and strong coupling).

II. Relativistically invariant theories, which may be divided into two groups: a) theories using the method of passage to the limit (the \(\lambda\)-method) for eliminating singular points in the solution of the equations of motion, in the classical formulation of the problem, and of the Schrödinger equations—in the quantum treatment; b) theories in which the question concerns finding new points of view on relativistically invariant representations, a radical example of which is the generalizing theories based on the Schrödinger equation (the theories of Heisenberg and Stueckelberg). Theories of the first type, in which the \(\lambda\)-method is used, were developed by the author of the review (G. Wentzel) and by P. A. M. Dirac *). Their peculiarity is that they refuse to consider the possibility of obtaining a finite law of conservation of energy and momentum, using only the concept of the field under consideration, i.e. they introduce the concept of a non-closed system. For the electromagnetic field this means the abandonment of the electromagnetic theory of mass.

The theories of Stueckelberg and Heisenberg are of considerably greater interest, since in them it is a matter of the successive further development of the principles of quantum theory, connected with the development and deepening of the ideas of the quantum-mechanical correspondence principle, according to which the development of the formalism presupposes first of all a critical analysis of the content of the available experimental problems and of the possibilities of their formulation.

Of the special problems considered are:

1. The problem of the quadrupole moment of the deuteron and the structure of the stable deuteron states.

2. The problem of calculating the values of the magnetic moment of the proton and neutron and the mass difference of the proton and neutron.

It must be regretted that the monograph completely lacks an analysis of applications of the theory to questions of the structure of heavy nuclei. It is also necessary to note the following shortcomings. A comparative analysis of the possible types

*) To this same class of theories one may also assign Heitler’s theory, which uses a peculiar method of subtracting infinities.

elementary particles (types of mesons) is directly connected with the question of the choice of the field Lagrangian (Pauli, Bhabha, Proca, Rosenfeld, de Broglie, and others) and of the commutation relations of dynamical variables. This question, directly related to one of the boundaries of applicability and the possibility of generalizing the Pauli principle*, remains entirely aside. Let us note that it is connected with the study of the very interesting question of introducing, in characterizing quantum systems, extremely abstract concepts of invariants of certain groups of transformations and, in particular, with the use of some of Weyl’s ideas on isomorphism of the transformation of symmetric groups and tensors. Further, among the shortcomings of the monograph one should include the fact that the question of the degree of definiteness of the meson remains unanalyzed; there are only a few, though very interesting, remarks on \(\beta\)-transformations and on the Klein and Jordan procedure, on the rearrangement of noncommutative operators by agreement and omission of the meson. Finally, let us note that the role of the static interaction is inevitably emphasized.

The appearance of this survey in Russian (as an appendix to G. Wentzel’s forthcoming book Introduction to the Quantum Theory of Wave Fields, State Publishing House for Technical-Theoretical Literature, 1947) should be welcomed.

K. V. Nikol’skii.