Mass Quantum Research Articles

Internal degrees and mass quantization for baryons and resonances

Vector radii apart from the angular momentum vector t are introduced into isospace, thereby permitting treatment of a system with structure in isospace. This also leads to unification of baryons on the foundations of internal dynamics, and the unified wave equation obtained for baryons permits transition to the corresponding field theory which is briefly discussed along with interactions. (D.C.W.)

Mass Quantization and Lepton Theory

Some features of mass quantization obtained by the introduction of a continuous inner degree of freedom into a free field are discussed. The usual particle interpretation, with discrete mass values, is applicable, as shown in the case of a second-quantized scalar field. A simple class of fermion field equations with unexpected lepton-like properties is also presented and studied in some detail. (auth)

Connection between the isorotator model of the hot particles and the d’Espagnat-Prentki theory

This paper deals with the connection between the screw model of the hot particles in isobaric spin space and the D' Espagnat-Prentkl theory. The theory says nothing about the rest mass of the elementary particle, whlle Rayski's theory leads in a very simple way to the mass quantization, though there are some arbitrary features in his model. It seems expedient to combine the positive properties of these theories. Rayski, however, provides the field quantity of the isorotator with two isospin indices corresponding to the isobaric spins of the two points. Fortunately, it can be shown that the eigenfunctions of the mass operator with respect to the rotations and inversions in isobaric spin space (u- space) transform as the D'Espagnat-Prentki's field quantities. This means a close connection between the two theories. In the proof use is made of the fact that the mass eigenequation must be covariant with respect to the rotations and inversions in u-space, which is very natural from the physical point of view.

Mass quantization in non-local field theory

Mass quantization in non-local field theory

Mass quantization and isotopic spin in non local-field theory

Starting from general remarks on the theory of fields, the local formulation of which seems to be insufficient, the author presents a non-local generalization of the Dirac equation that leads, by means of convenient supplementary conditions, to a mass spectrum for the particles of spin 1/2. The analogies of this mass spectrum with those obtained from the Yukawa and Pais theories are discussed.

Isotopic spin and mass quantization

In studying π - H collisions, the cosmotron group has meanwhile found two cases of V 1 / 0 -production. Assuming π + H → V 1 / 0 + one neutral particle, the latter would have to be a heavy meson in both cases, (mass ~ 1300 mine ) with a life time > 4.10 10 sec. This reaction may correspond to π + H → V 1 / 0 + Π 0 in the present picture. Furthermore one case has been observed of the production of a V 1 with charge e . The existence of V 1 − would necessitate that 2 P 3/2 rather than 2 P 1/2 is the next lowest state, corresponding to Λ ≈0,45 ħ /Mc. This new situation would not alter any of the qualitative results of this work.

The Irreducible Volume Character of Events. I. A Theory of the Elementary Particles and of Fundamental Length

In this series of papers a theory of elementary particles is presented based on the postulates that the elementary particles are a material process and that with every such process there is associated an inherent irreducible volume of space-time. The equations of motion are obtained from the wave equations of Dirac, Maxwell, etc., through a two-step correspondence principle consisting of replacing these equations by self-adjoint partial difference equations and then integrating these over the group manifold of the closed real orthogonal group $G$ in four-dimensional space. This introduces a new fundamental constant of the dimensions of a length, the difference step $\ensuremath{\omega}$. The resulting equations are relativistically invariant integro-difference equations in a complex four-dimensional space. They give a quantized mass spectrum when $\ensuremath{\omega}$ is purely imaginary. This paper treats only the Dirac equation. Section 1 sketches the basic physical ideas from which we work. Section 2 carries out the mathematical realization of the ideas of Section 1, obtains the fundamental integro-difference equation (2.2) for spin \textonehalf{} processes, points out that space is a fourdimensional complex continuum, and defines the dynasphere. Section 3 transforms the integro-difference equation into an equivalent partial differential equation of infinite order (3.10). The operator functions in (3.10) are the Bessel functions ${J}_{1}(z)$ and ${J}_{2}(z)$ when the radius ($i\ensuremath{\omega}$) of the dynasphere is purely imaginary. Section 4 gives the general solution of (3.10) and deduces the mass quantization condition. In keeping with our basic postulates all elementary charged particles of spin \textonehalf{} must be embraced by this mass quantization condition which is the case for the electron, proton, and $\ensuremath{\mu}$-meson (predicted mass 218.76 e.m.u. [electron mass units]) with the fundamental length $\ensuremath{\omega}=4.538\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}13}$ cm (one-half percent larger than the classical electron diameter). This possibility is due to the rather remarkable properties of the mass quantization condition (4.4). There is an infinite number of roots not uniformly spaced and indeed not uniformly non-uniform in this respect: first there is one very small positive root which gives the electron; the next positive root reaches way out to give on a mass scale the $\ensuremath{\mu}$-meson at 218 e.m.u.; the distance on the mass scale to the next root suffers a sudden drop to 139 e.m.u., the spacing thereafter dropping uniformly to the asymptotic value of 133.69 e.m.u. The proton is the thirteenth in the series. Table I of this section lists the first sixteen masses. All of these particles have the same magnitude of electronic charge since they are just different states of the same matter equation. Section 5 gives two alternatives for the neutral particles. In one we simply set the charge to zero and obtain one zero mass particle and an infinite number close in mass to those of the charged particles (the electron excluded). In the other we further change to a real radius for the dynasphere, in which case we have only one real zero mass. On this alternative we have only one elementary neutral particle of spin \textonehalf{}---the neutrino---and (combined with Section 4) the only elementary particles with non-vanishing rest mass are charged (and conversely), the universality of charge being simply identified with the existence of the particle. Since there is no neutral particle between the neutrino and the $\ensuremath{\mu}$-meson on either alternative we can predict that the ${\ensuremath{\mu}}^{0}$-particle postulated by Tiomno and Wheeler for the decay of the $\ensuremath{\mu}$-meson must be a neutrino, that is, $\ensuremath{\mu}\ensuremath{\rightarrow}e+2\ensuremath{\nu}$.

On the Quantization of Mass

The Dirac equation may be written so as to give an eigenvalue problem whose eigenvalues would be values of the electron mass. The equation is solved in several cosmological spaces, none requiring any quantization of $m$. A space-time suggested by Eddington leads to wave equations that have solutions with quantized $m$, $m$ depending upon the radius of the universe, constants $c$ and $\ensuremath{\hbar}$, and a quantum number. If the radius of the universe is taken as ${10}^{28}$ cm, the lowest mass state in this group of solutions is of the order of ${10}^{\ensuremath{-}65}$ g. Conversely if the usual electron mass is considered as the lowest state, the radius of the universe is of the order of ${10}^{\ensuremath{-}10}$ cm. Since the only constants occurring in the theory are $\ensuremath{\hbar}$, $m$, and $c$, one would expect that the radius of the universe would come out in terms of $\frac{h}{\mathrm{mc}}$. Only an occurrence, as the result of quantization, of a large dimensionless number could lead to a reasonable result; but Dirac's equation evidently does not provide such a number, and is therefore unsuited to account for the electron mass in terms of the radius of the universe.