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.

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.

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.

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

Resonant Frequency and Sensitivity of an AFM Microcantilever Modeled by the Non-Local Theory

2011 ◽  
Author(s):  
E. Khosravani ◽  
M. H. Kahrobaiyan ◽  
M. T. Ahmadian
Keyword(s):  
Resonant Frequency ◽  
Classical Theory ◽  
Variational Approach ◽  
Contact Stiffness ◽  
Current Model ◽  
Equation Of Motion ◽  
Local Theory ◽  
Local Parameter ◽  
Non Local ◽  
The Difference

In this paper, utilizing the non-local theory, the resonant frequency and sensitivity of an AFM microcantilever are investigated. To that end, the governing equation of motion and corresponding boundary conditions are obtained using the variational approach. Afterwards, the resonant frequency and sensitivity of the AFM microcantilever are derived analytically and depicted in some figures versus the contact stiffness of the sampling surface. The results of the current model are compared to those of the classical theory. The comparison shows that the difference between the results of the non-local theory and those of the classical theory is significant when the non-local parameter is high but it diminishes as the non-local parameter decreases.

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.

scholarly journals Diluted mass gap in strongly coupled non-local Yang-Mills

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Marco Frasca ◽  
Anish Ghoshal
Keyword(s):  
Field Theory ◽  
Particle Physics ◽  
Mass Scale ◽  
Local Theory ◽  
Quantum Field ◽  
Strongly Coupled ◽  
Yang Mills ◽  
Mass Gap ◽  
Non Local ◽  
Non Locality

Abstract We investigate the non-perturbative regimes in the class of non-Abelian theories that have been proposed as an ultraviolet completion of 4-D Quantum Field Theory (QFT) generalizing the kinetic energy operators to an infinite series of higher-order derivatives inspired by string field theory. We prove that, at the non-perturbative level, the physical spectrum of the theory is actually corrected by the “infinite number of derivatives” present in the action. We derive a set of Dyson-Schwinger equations in differential form, for correlation functions till two-points, the solution for which are known in the local theory. We obtain that just like in the local theory, the non-local counterpart displays a mass gap, depending also on the mass scale of non-locality, and show that it is damped in the deep UV asymptotically. We point out some possible implications of our result in particle physics and cosmology and discuss aspects of non-local QCD-like scenarios.

scholarly journals Non-Local Theory of Nucleon-Meson Field

1952 ◽  
Vol 8 (1) ◽  
pp. 133-134
Author(s):  
N. Shono
Keyword(s):  
Local Theory ◽  
Meson Field ◽  
Non Local

Study of internal stresses in rock massif within the framework of elastic layered block models with inclusions of the hierarchical structure of the L-rank.

2021 ◽  
Author(s):  
Olga Hachay ◽  
Andrey Khachay
Keyword(s):  
Hierarchical Structure ◽  
Classical Theory ◽  
Acoustic Waves ◽  
Degrees Of Freedom ◽  
Heterogeneous Media ◽  
Theory Of Elasticity ◽  
Rock Massif ◽  
Local Theory ◽  
Internal Stresses ◽  
Non Local

<p>In recent years, new models of continuum mechanics, generalizing the classical theory of elasticity, have been intensively developed. These models are used to describe composite and statistically heterogeneous media, new structural materials, as well as in complex massifs in mine conditions. The paper presents an algorithm for the propagation of longitudinal acoustic waves in the framework of active well monitoring of elastic layered block media with inclusions of hierarchical type of L-th rank. Relations for internal stresses and strains for each hierarchical rank are obtained, which constitute the non local theory of elasticity. The essential differences between the non local theory of elasticity and the classical one and the connection between them are investigated. A characteristic feature of the theory of media with a hierarchical structure is the presence of scale parameters in explicit or implicit form. This work focuses on the study of the effects of non locality and internal degrees of freedom, reflected in internal stresses, which are not described by the classical theory of elasticity and which can be potential precursors of the development of a catastrophic process in a rock massif. Thanks to the use of a model of a layered block medium with hierarchical inclusions, it is possible, using borehole acoustic monitoring, to determine the position of the highest values ​​of internal stresses and, with less effort, to implement the method of unloading the rock massif. If it is necessary to conduct short-term predictive monitoring of geodynamic regions and determine a more accurate position of the source of a dynamic phenomenon using borehole active acoustic observations, it is necessary to use the values ​​of the tensor of internal hierarchical stresses as a monitored parameter.</p>

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