Construction of an elementary particle theory in cosmological spaces

Using the system of enclosure, a four-dimensional curved (conformai) space is inserted in a six-dimensional plane space, where it occupies some surface. Based upon the symmetry of the surface indicated, the equation of the scalar field on the surface is written. Thereupon, using the enclosure formula, the equation obtained is transcribed into the original four-dimensional space. It is shown that the well-known scalar field equation obtained by other authors is a particular case of the equation obtained in this study.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii Fizika, No. 10, pp. 79–83, October, 1971.The authors express their gratitude to Professor D. Ivanenko for his discussion of the question.     

Applications of catastrophe theory to the physical sciences

Catastrophe Theory was introduced by René Thom in the late 1960's, as an attempt to model morphogentic changes in nature using ideas from topological dynamics and the theory of singularities of mappings. Thom envisaged a very general approach to topological changes in the solutions to parametrized systems of equations (such as differential and difference equations), and in particular discussed the special case of ‘elementary’ catastrophe theory: singularities of smooth real-valued functions. Popular expositions have tended to overemphasize this special case, but it remains the major source of ideas and methods.Here we survey the applications of Catastrophe Theory to the physical sciences (physics, chemistry, engineering, fluid mechanics, etc.). For brevity we confine attention to an area lying between ‘elementary’ and ‘general’ Catastrophe Theory, usually known as Singularity Theory. This is the theory of singularities of smooth vector-valued functions, which mathematically is a straightforward (though non-trivial) generalization of the real-valued case. In the last few years it has developed into a powerful and useful technique in several areas of theoretical physics, notably optics and bifurcation theory. Equivariant Catastrophe Theory, taking account of symmetry, is likely to prove especially interesting.     

A class of nonlinear relativistic partial differential equations in elementary particle theory

In mathematical approaches to elementary particle theory, the equation [² - ²/t²]=m² ;+g ³ has been of interest [1,2]; it describes a quartically self-coupled neutral scalar meson field. This paper applies the decomposition method [3-6] to obtain accurate non-perturbative timedevelopment of the field for this equation, or variations involving other nonlinear interactions, without the use of cutoff functions or truncations.     

The lifetime of an elementary particle in a field

By assuming that we can associate a proper frame to a particle in a field and using relativistic considerations, a generalization of Apsel's prediction that electromagnetic potentials can alter the lifetime of a charged particle is obtained. It is shown, by a new procedure, that these same assumptions lead to the Euler-Lagrange equations of motion for the particle. This result seems to disclose a deep connection between kinematical and dynamical aspects of motion.     

Unravelling combustion mechanisms through a quantitative understanding of elementary reactions

This review of the role of reaction kinetics in combustion chemistry traces the historical evolution and present state of qualitative and quantitative understanding of a number of reaction systems. Starting from the H₂–O₂ system, in particular from the reaction between H and O₂, mechanisms and key reactions for soot formation, for the appearance of NO_x, and for processes of peroxy radicals in hydrocarbon oxidation are illustrated. The struggle for precise rate constants on the experimental and theoretical side is demonstrated for the example of the reaction H + O₂ → OH + O. The intrinsic complexity of complex-forming bimolecular reactions, such as observed even in this reaction, also dominates most other key reactions of the systems considered and can be unravelled only with the help of quantum-chemical methods. The multi-channel character of these reactions often also requires the combination with master equation codes. Although kinetics provides an already impressive database for quantitative modelling of simple combustion systems, considerable effort is still required to quantitatively account for the complexities of more complicated fuel oxidation processes.     

The stability of fundamental constants

The tests of the constancy of fundamental constants are tests of the local position invariance and thus of the equivalence principle, at the heart of general relativity. After summarising the links between fundamental constants, gravity, cosmology and metrology, a brief overview of the observational and experimental constraints on their variation is proposed.     

A new approach to the theory of elementary domains

It is shown that Yukawa's theory of elementary domains can be formulated in a general framework. A quantized measure space structure of a space-time manifold is introduced so as to represent faithfully the elementary-domain structure. For a realization of elementary domains, an operator valued measure is defined such that it represents the spatiotemporal distribution of elementary domains. Effects of such a quantized topology are illustrated in the expressions ofS matrices.     

Structure of elementary particles in a nonlinear field theory

Characteristics of nonlinear gauge-invariant singularity-free field theories of elementary particles are discussed. It is shown that the electromagnetic field, in conjunction with a scalar field which is required for gauge invariance, provides a potential mechanism for the creation of the spin and magnetic moment of the particle, in addition to its mass and charge.     

Geometro-stochastic quantization of a theory for extended elementary objects

The geometro-stochastic quantization of a gauge theory based on the (4,1)-de Sitter group is presented. The theory contains an intrinsic elementary length parameter R of geometric origin taken to be of a size typical for hadron physics. Use is made of a soldered Hilbert bundle over curved spacetime carrying a phase space representation of SO(4, 1) with the Lorentz subgroup related to a vierbein formulation of gravitation. The typical fiber of is a resolution kernel Hilbert space constructed in terms of generalized coherent states related to the principal series of unitary irreducible representations of SO(4, 1), namely de Sitter horospherical waves for spinless particles characterized by the parameter . The framework is, finally, extended to a quantum field-theoretical formalism by using bundles with Fock space fibers constructed from .Supported in part by NSERC Research Grant No. A5206.     

A three-wave model of the elementary particle

The physical ideas that led the author to propose the “three-wave hypothesis” (TWH) are presented. Some new interpretative elements are introduced.     

An electromagnetic inertial mass theory applied to elementary particles

A definition of inertial mass is advanced which views this mass property as being due to intrinsic periodic electromagnetic processes characterized by an amplitudeR and an angular frequencyω. The existence of a stableE/M composite mass unit, called a hylon, is then postulated composed of two or more of these primitive processes. Selected space-time coherence relations are then imposed onω andR through ad hoc quantizations based on notions borrowed from historical physical theories. Elementary particles are then investigated to test the efficacy of the mass definition and coherence relations. It is found that by equating the postulated hylon mass with the experimental pion masses, a mass spectrum emerges which has a close correspondence with many of the more stable particles and resonances. A case is then made for considering these particles as being primarily electromagnetic in nature and exhibiting an underlying space-time structure in terms of the theory advanced.     

Roll stability catastrophe mechanism of a flooded ship on regular sea waves

Based on a typical one-free-degree ship roll motion equation, the cusp catastrophe model is built including the bifurca- tion set equation, splitting factor ＇u＇ and regular factor ＇v＇, where both ＇u＇ and ＇v＇ are further expressed with typical flooded ship parameters. Then, the roll catastrophe mechanism is analyzed mainly by means of ＇u＇, under the given parameters of a typical trawler boat. The aim of this research is to reveal the mutagenic mechanism of the roll stability and provide a reference for improving ship roll stability.     

Interaction in scalar field theory with a fundamental length

A certain generalization is considered of the apparatus of quantum field theory in a momentum space of constant curvature. The passage to a configuration representation is accomplished by using a Fourier transformation in terms of plane waves of pseudo-Euclidean five-space. In momentum space de Sitter constructed a model of the interaction between complex and real scalar fields and the corresponding graphical technique.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 58–63, April, 1984.     

Quantum theory of a massless spinning particle

The classical and quantum mechanics of a free massless point-like fermion is presented. The action is invariant under local 1-dimensional reparametrizations and supersymmetry, as well as a large set of rigid symmetries, including conformal and chiral symmetries. An infinite set of rigid symmetries is derived starting from the chiral invariance, but only a finite subset does not vanish on shell. The BRST-transformations corresponding to thed=1 local symmetries are constructed and the quantization is performed. Finally, the BRST-cohomology is investigated and the conditions producing the physical states are derived.     

A theory of elementary couplings III

We further develop a recent method, based on compensation between Feynman diagrams, for obtaining a priori information on the spectrum and interactions (weak and strong) of the elementary particles. The theory is based on hadron octets or nonets of spin zero and one half, together with vector bosons including photons. It has the necessary ingredients of a realistic broken-symmetry gauge theory, the compensation method giving the rules for breaking the symmetry. In this article, the scope of the compensation principle is greatly enlarged, thanks to the inclusion of scalar mesons. The main point of this paper is to show in detail how the strong (Yukawa) couplings may be completely determined by the compensation relations. The numerical results are worked out in the limit of exact SU(3) for the weak couplings. The eta and charged kaon lifetimes can now be computed, and come out in fair agreement with the data. The strong ΣΛπ coupling is no longer zero, as in parts I and II, but is still smaller than the current experimental estimates. The accurate mass formula N^?1+Ξ^?1+Σ^?1 = 6(N+Ξ)^?1 is rederived in a new framework, and appears to be connected with a simple SU(3)-breaking weak or superweak interaction.     

A new theory of elementary matter

This is the first of a series of articles that reviews and expands upon a new theory of elementary matter. This paper presents an exposition of the philosophical approach and its general implications. The ensuing explicit form of the mathematical expression of the theory and several applications in the atomic and elementary particle domains will be developed in the succeeding parts of this series.The theory is based on three axioms: the principle of general relativity, a generalized Mach principle, and a correspondence principle. The approach is basically a deterministic, relativistic field theory which fully incorporates the idea that any realistic physical system is in facta closed system, without separable parts. It is shown that the most primitive mathematical expression of this theory, following as anecessary consequence of its axioms, is in terms of a set of coupled nonlinear spinor field equations. Nevertheless, the exact formalism is constructed to asymptotically approach the quantum mechanical formalism for a many-particle system, in the limit of sufficiently small energy-momentum transfer among the components of the considered closed system. Thus, all of the mathematical predictions of nonrelativistic quantum mechanics are contained in this theory, as a mathematical approximation. However, predictions follow from the exact form of this theory (where energy-momentum transfer can be arbitrarily large) that are not contained in the quantum theory.