The Problem of Runaway Solutions in the Lorentz-Dirac Theory

1976 ◽  
Vol 31 (7) ◽  
pp. 683-689
Author(s):  
M. Sorg
Keyword(s):  
Dirac Equation ◽  
General Theory ◽  
Finite Size ◽  
Finite Extension ◽  
Point Of View ◽  
Existence Proof ◽  
Dirac Theory ◽  
Hyperbolic Motion ◽  
Size Model

Abstract A rigorous non-existence proof for runaway solutions in the finite-size model of the electron is given. Since a consistent point limit, such as the Lorentz-Dirac equation claims to be, should not exhibit features which are completely missing in the more general theory of finite extension, it is proposed that the point-like approximation of the finite-size theory be the integrodifferential formulation of the Lorentz-Dirac theory. This point of view is supported by a new discussion of the hyperbolic motion in the latter theory.

Classical, Covariant Finite-size Model of the Radiating Electron

1974 ◽  
Vol 29 (11) ◽  
pp. 1671-1684 ◽  
Author(s):  
M. Sorg
Keyword(s):  
Dirac Equation ◽  
Finite Size ◽  
Finite Extension ◽  
Equation Of Motion ◽  
Mass Renormalization ◽  
Classical Electron ◽  
Size Model

The finite extension of the classical electron is defined in a new, covariant manner. This new definition enables one to calculate exactly the bound and emitted four-momentum and to find an equation of motion different from the Lorentz-Dirac equation and from other equations proposed in the literature. Neither mass renormalization nor use of advanced quantities nor asymptotic conditions are necessary. Runaway solutions and pre-acceleration do not occur in the framework of the model presented here.

Hyperbolic Motion in the Finite-size Model of the Radiating Electron

1975 ◽  
Vol 30 (12) ◽  
pp. 1535-1542
Author(s):  
M. Sorg
Keyword(s):  
Exact Solution ◽  
Field Strength ◽  
External Field ◽  
Critical Phenomena ◽  
Finite Size ◽  
Momentum Balance ◽  
Hyperbolic Motion ◽  
Size Model

Abstract Within the framework of the finite-size model of the electron recently dovelopped the case of hyperbolic motion is studied rigorously by means of an exact solution. The energy-momentum balance is discussed as well as the critical phenomena arising if the external field strength comes into the range of order of the maximal self-field strength of the particle. It is found that the commonly accepted Lorentz-Dirac-Rohrlich theory is only a good approximation for small values of the external field strength.

scholarly journals TOPOLOGICAL INSULATOR AND THE DIRAC EQUATION

SPIN ◽  
2011 ◽  
Vol 01 (01) ◽  
pp. 33-44 ◽  
Author(s):  
SHUN-QING SHEN ◽  
WEN-YU SHAN ◽  
HAI-ZHOU LU
Keyword(s):  
Dirac Equation ◽  
Topological Insulator ◽  
Bound States ◽  
Topological Insulators ◽  
Mass Term ◽  
Point Of View ◽  
Quadratic Term ◽  
General Description ◽  
Dirac Equations ◽  
Topological Quantum

We present a general description of topological insulators from the point of view of Dirac equations. The Z2 index for the Dirac equation is always zero, and thus the Dirac equation is topologically trivial. After the quadratic term in momentum is introduced to correct the mass term m or the band gap of the Dirac equation, i.e., m → m − Bp2, the Z2 index is modified as 1 for mB > 0 and 0 for mB < 0. For a fixed B there exists a topological quantum phase transition from a topologically trivial system to a nontrivial system when the sign of mass m changes. A series of solutions near the boundary in the modified Dirac equation is obtained, which is characteristic of topological insulator. From the solutions of the bound states and the Z2 index we establish a relation between the Dirac equation and topological insulators.

scholarly journals The wave pattern of a doublet in a stream

1928 ◽  
Vol 121 (788) ◽  
pp. 515-523 ◽  
Keyword(s):  
Surface Effect ◽  
Ideal Point ◽  
Finite Size ◽  
Wave Pattern ◽  
Wave Resistance ◽  
Point Of View ◽  
The Body ◽  
Surface Elevation ◽  
More Care ◽  
Forced Waves

The following paper is a study of the surface waves caused by a doublet in a uniform stream, and in particular the variation in the pattern with the velocity of the stream or the depth of the doublet. In most recent work on this subject attention has been directed more to the wave resistance, which can be evaluated with less difficulty than is involved in a detailed study of the waves; in fact, it would seem that it is not necessary for that purpose to know the surface elevation completely, but only certain significant terms at large distances from the disturbance. Recent experimental work has shown con­siderable agreement between theoretical expressions for wave resistance and results for ship models of simple form, and attempts have been made at a similar comparison for the surface elevation in the neighbourhood of the ship. In the latter respect it may be necessary to examine expressions for the surface elevation with more care, as they are not quite determinate; any suitable free disturbance may be superposed upon the forced waves. For instance, it is well known that in a frictionless liquid a possible solution is one which gives waves in advance as well as in the rear of the ship, and the practical solution is obtained by superposing free waves which annul those in advance, or by some equivalent artifice. This process is simple and definite for an ideal point disturbance, but for a body of finite size or a distributed disturbance the complete surface elevation in the neighbourhood of the body requires more careful specification as regards the local part due to each element. It had been intended to consider some expressions specially from this point of view, but as the matter stands at present it would entail a very great amount of numerical calculation, and the present paper is limited to a much simpler problem although also involving considerable computation. A horizontal doublet of given moment is at a depth f below the surface of a stream of velocity c ; the surface effect may be described as a local disturbance symmetrical fore and aft of the doublet together with waves to the rear. Two points are made in the following work.

LEGAL STATUS OF THE SOLE EXECUTIVE BODY OF A LIMITED LIABILITY COMPANY

2021 ◽  
Author(s):  
Yulia Fanilevna Aitova ◽  
Keyword(s):  
General Theory ◽  
Legal Status ◽  
Limited Liability ◽  
Point Of View ◽  
Limited Liability Company ◽  
Points Of View ◽  
Theory Of Law ◽  
The Individual ◽  
Executive Body

The article analyzes the issue of determining the legal status of the individual management body of a limited liability company. The author begins his research with the concept of legal status existing in the general theory of law, and then proceeds to consider the issue from the point of view of philosophical categories. In addition, the work explores the diversity of points of view existing in the doctrine regarding the legal status of the individual management body of economic societies.

scholarly journals Nature itself in a mirror space–time

2015 ◽  
Vol 93 (10) ◽  
pp. 1005-1008 ◽  
Author(s):  
Rasulkhozha S. Sharafiddinov
Keyword(s):  
Dirac Equation ◽  
Minkowski Space ◽  
Space Time ◽  
Point Of View ◽  
Classical Solutions ◽  
Left Handed ◽  
Minkowski Space Time ◽  
Energy And Momentum ◽  
The Right ◽  
Structure Of Matter

The unity of the structure of matter fields with flavor symmetry laws involves that the left-handed neutrino in the field of emission can be converted into a right-handed one and vice versa. These transitions together with classical solutions of the Dirac equation testify in favor of the unidenticality of masses, energies, and momenta of neutrinos of the different components. If we recognize such a difference in masses, energies, and momenta, accepting its ideas about that the left-handed neutrino and the right-handed antineutrino refer to long-lived leptons, and the right-handed neutrino and the left-handed antineutrino are short-lived fermions, we would follow the mathematical logic of the Dirac equation in the presence of the flavor symmetrical mass, energy, and momentum matrices. From their point of view, nature itself separates Minkowski space into left and right spaces concerning a certain middle dynamical line. Thereby, it characterizes any Dirac particle both by left and by right space–time coordinates. It is not excluded therefore that whatever the main purposes each of earlier experiments about sterile neutrinos, namely, about right-handed short-lived neutrinos may serve as the source of facts confirming the existence of a mirror Minkowski space–time.

Profinite Modules

1973 ◽  
Vol 16 (3) ◽  
pp. 405-415
Author(s):  
Gerard Elie Cohen
Keyword(s):  
Finite Group ◽  
General Theory ◽  
Finite Length ◽  
Finite Groups ◽  
Inverse Limit ◽  
Abelian Groups ◽  
Point Of View ◽  
Inverse Limits ◽  
Profinite Groups ◽  
Inverse Systems

An inverse limit of finite groups has been called in the literature a pro-finite group and we have extensive studies of profinite groups from the cohomological point of view by J. P. Serre. The general theory of non-abelian modules has not yet been developed and therefore we consider a generalization of profinite abelian groups. We study inverse systems of discrete finite length R-modules. Profinite modules are inverse limits of discrete finite length R-modules with the inverse limit topology.

scholarly journals Perspectives pour la linguistique : de la linguistique descriptive à la linguistique explicative

2021 ◽  
Vol 33 ◽  
pp. 1-29
Author(s):  
Wiesław Banyś
Keyword(s):  
General Theory ◽  
Point Of View ◽  
Primitive Elements ◽  
Aim Of Science ◽  
The Difference ◽  
Main Components ◽  
General Linguistic ◽  
Object Of Study ◽  
Comprehensive Study

The text deals with one of the challenges of linguistics, which is to effectively combine description and explanation in linguistics.It is necessary that linguistic theories are not only capable of adequately describing their object of study within their framework, but they must also have a suitable explanatory power.Linguistics centred around the explanation of the why of the system is called here ‘explanatory’ or ‘non-autonomous’, in contrast to ‘descriptive’ or ‘autonomous’ linguistics, which is focused on the description of the system, the distinction being based on the difference in the objects of study, the goals and the descriptive and explanatory possibilities of the theories.From the point of view presented here, a comprehensive study of language has three main components: a general theory of what language is, a resulting theory and description, which is a function of this theory, of how language is organised, functions and has evolved in the human brain, and an explanation of the properties of language found.The explanatory value of a general linguistic theory is a function of various elements, among others, the quantity of the primitive elements of the theory adopted and the effectiveness of Ockham’s razor principle of simplicity. It is also a function of the quality of those elements which can be drawn not only from within the system, but also from outside the system becoming in this situation logically prior to the object under study.In science, in linguistics, one naturally needs two types of approach, two types of linguistics, descriptive/autonomous and explanatory/non-autonomous, one must first describe reality in order to explain it. But it is also certain that since the aim of science is to explain in order to reach that higher level of scientificity above pure description, it is necessary that this aim be realized in different linguistic theories within different research programs, uniting descriptivist and explanatory approaches.

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