Non-local Generalization of the Lorentz-Dirac Equation and the Problem of Runaway Solutions

1976 ◽  
Vol 31 (6) ◽  
pp. 664-665 ◽  
Author(s):  
M. Sorg
Keyword(s):  
Dirac Equation ◽  
Finite Extension ◽  
Equation Of Motion ◽  
Covariant Equation ◽  
Non Local ◽  
New Equation

A new, covariant equation of motion for the radiating electron of finite extension is proposed. This new equation excludes the notorious runaway solutions and pre-acceleration

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.

Causality Violation and Non-local Generalization of the Lorentz-Dirac Equation

1977 ◽  
Vol 32 (3-4) ◽  
pp. 319-326
Author(s):  
P. Alber ◽  
W. Heudorfer ◽  
M. Sorg
Keyword(s):  
Dirac Equation ◽  
Equation Of Motion ◽  
Local Theory ◽  
Constant Force ◽  
Dirac Theory ◽  
Local Equation ◽  
Causality Violation ◽  
Finite Duration ◽  
Non Local

AbstractIt is demonstrated by a concrete example (constant force of finite duration) that the recently proposed, non-local equation of motion for the radiating electron does exhibit the effect of causality violation. This phenomenon, which occurs in the non-local theory in form of self-oscillations, is however less severe than in the Lorentz-Dirac theory, if only physically reasonable forces are admitted.

A new equation of motion for a radiating charged particle

1974 ◽  
Vol 337 (1611) ◽  
pp. 591-598 ◽  
Keyword(s):  
Charged Particle ◽  
Dirac Equation ◽  
Point Charge ◽  
Equation Of Motion ◽  
Second Order ◽  
Radiated Energy ◽  
Proper Mass ◽  
New Equation

A new equation of motion for a classical radiating point-charge is proposed. The radiated energy is supplied by a reduction in proper-mass of the particle. Unlike the Lorentz–Dirac equation, the equation proposed is second order: it gives physically reasonable predictions, and in particular has no runaway solutions and no pre-acceleration.

Finite Size of the Electron and Runaway Solutions

1977 ◽  
Vol 32 (5) ◽  
pp. 383-389 ◽  
Author(s):  
J. Petzold ◽  
W. Heudorfer ◽  
M. Sorg
Keyword(s):  
Dirac Equation ◽  
Free Electron ◽  
Constant Velocity ◽  
Initial Conditions ◽  
Perturbation Expansion ◽  
Finite Size ◽  
Equation Of Motion ◽  
Local Equation ◽  
Causality Violation ◽  
Non Local

Abstract The problem of runaway solutions is studied within the framework of a non-local equation of motion for the classically radiating electron. It is found that the force-free electron oscillates down to a constant velocity under emission of radiation, if certain restrictions on the initial conditions are imposed. Causality violation is not present in this model, but penetrates into the theory as consequence of a false perturbation expansion leading to the notorious Lorentz-Dirac equation of motion.

Classical Electrodynamics and Acoustics: Sound Radiation by Moving Multipoles

1997 ◽  
Vol 119 (2) ◽  
pp. 271-282 ◽  
Author(s):  
G. C. Gaunaurd ◽  
T. J. Eisler
Keyword(s):  
Dirac Equation ◽  
Free Field ◽  
Sound Radiation ◽  
Equation Of Motion ◽  
Rotating Machinery ◽  
Classical Electrodynamics ◽  
Radiation Patterns ◽  
Frequency Distributions ◽  
Acoustic Sources ◽  
Power Radiation

In classical electrodynamics (CED) P. Dirac used the average of retarded and advanced fields to represent the bound field and their difference to represent the free field in his derivation of the (Lorentz-Dirac) equation of motion for an electron. The latter skew-symmetric combination filtered out the radiation part of the field. It can also be used to derive many properties of the power radiated by acoustic sources, such as angular and frequency distributions. As in CED there is radiation due to source acceleration and radiation patterns exhibit the “headlight effect.” Power radiation patterns are obtained by this approach for point multipoles undergoing various motions. Applications to sound radiation problems from rotating machinery are shown. Numerous computed plots illustrate all cases.

scholarly journals Oscillating scalar dissipating in a medium

2021 ◽  
Vol 2021 (11) ◽  
Author(s):  
Wen-Yuan Ai ◽  
Marco Drewes ◽  
Dražen Glavan ◽  
Jan Hajer
Keyword(s):  
Perturbation Theory ◽  
Quantitative Description ◽  
Early Time ◽  
Scalar Fields ◽  
Equation Of Motion ◽  
Time Dependent ◽  
Local Equation ◽  
Starting Point ◽  
Non Linear ◽  
Non Local

Abstract We study how oscillations of a scalar field condensate are damped due to dissipative effects in a thermal medium. Our starting point is a non-linear and non-local condensate equation of motion descending from a 2PI-resummed effective action derived in the Schwinger-Keldysh formalism appropriate for non-equilibrium quantum field theory. We solve this non-local equation by means of multiple-scale perturbation theory appropriate for time-dependent systems, obtaining approximate analytic solutions valid for very long times. The non-linear effects lead to power-law damping of oscillations, that at late times transition to exponentially damped ones characteristic for linear systems. These solutions describe the evolution very well, as we demonstrate numerically in a number of examples. We then approximate the non-local equation of motion by a Markovianised one, resolving the ambiguities appearing in the process, and solve it utilizing the same methods to find the very same leading approximate solution. This comparison justifies the use of Markovian equations at leading order. The standard time-dependent perturbation theory in comparison is not capable of describing the non-linear condensate evolution beyond the early time regime of negligible damping. The macroscopic evolution of the condensate is interpreted in terms of microphysical particle processes. Our results have implications for the quantitative description of the decay of cosmological scalar fields in the early Universe, and may also be applied to other physical systems.

Initial-Value Problem for the Non-local Generalization of the Lorentz-Dirac Equation

1976 ◽  
Vol 31 (12) ◽  
pp. 1457-1464
Author(s):  
M. Sorg
Keyword(s):  
Proper Time ◽  
Perturbation Expansion ◽  
Equation Of Motion ◽  
Successive Approximations ◽  
Method Of Successive Approximations ◽  
Dirac Theory ◽  
Initial Value ◽  
Local Character ◽  
Non Local ◽  
Non Locality

AbstractAlthough the equation of motion, recently proposed for the classical radiating electron, is of non-local character in proper time, the Newtonian initial data (position and velocity) are sufficient to guarantee existence and uniqueness of the solutions. The corresponding existence proof is accomplished by the Picard-Lindelöf method of successive approximations. This method indicates the possibility of a perturbation expansion of the exact solution in terms of the non-locality parameter. Such a perturbation expansion does not seem to be possible in the Lorentz-Dirac theory.

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.

scholarly journals Energy dissipation for hereditary and energy conservation for non-local fractional wave equations

2020 ◽  
Vol 378 (2172) ◽  
pp. 20190295 ◽  
Author(s):  
Dušan Zorica ◽  
Ljubica Oparnica
Keyword(s):  
Energy Dissipation ◽  
Energy Conservation ◽  
Wave Equations ◽  
A Priori ◽  
Constitutive Models ◽  
Equation Of Motion ◽  
Constitutive Law ◽  
Energy Estimates ◽  
Fractional Wave Equations ◽  
Non Local

Using the method of a priori energy estimates, energy dissipation is proved for the class of hereditary fractional wave equations, obtained through the system of equations consisting of equation of motion, strain and fractional order constitutive models, that include the distributed-order constitutive law in which the integration is performed from zero to one generalizing all linear constitutive models of fractional and integer orders, as well as for the thermodynamically consistent fractional Burgers models, where the orders of fractional differentiation are up to the second order. In the case of non-local fractional wave equations, obtained using non-local constitutive models of Hooke- and Eringen-type in addition to the equation of motion and strain, a priori energy estimates yield the energy conservation, with the reinterpreted notion of the potential energy. This article is part of the theme issue ‘Advanced materials modelling via fractional calculus: challenges and perspectives’.

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