Radiation reaction in 2+1 electrodynamics

Yaremko, Yurij

doi:10.1063/1.2779765

Cited by 8 publications

(8 citation statements)

References 21 publications

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“…This is why in the most of the existing literature only the even-dimensional radiation problems were considered [17,[22][23][24][25][26] . The case of odd dimensions was discussed mainly in the context of the radiation reaction problem [27][28][29][30][31][32][33], see also the reviews [34,35]. Meanwhile, the radiation reaction in dimensions other than four, creates additional problems.…”

Section: Introductionmentioning

confidence: 99%

Synchrotron radiation in odd dimensions

Gal'Tsov

Khlopunov

2020

Phys. Rev. D

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In odd space-time dimensions, the retarded solution of the massless wave equation has support not only on the light cone, but also inside it. At the same time, a free massless field should propagate at the speed of light. The apparent contradiction of these two features is resolved by the fact that the emitted part of the field in the wave zone depends on the history of motion up to the retarded moment of proper time. It is shown that in the case of circular motion with ultrarelativistic velocity, the main contribution to the radiation amplitude is made by a small interval of proper time preceding the retarded time, and thus the tail term is effectively localized. We obtain a tentative formula for scalar synchrotron radiation in D dimensions: P = g 2 (ω 0 γ 2 / √ 3) D−2 , which is explicitly verified in D = 3, 4, 5.

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Section: Introductionmentioning

confidence: 99%

Synchrotron radiation in odd dimensions

Gal'Tsov

Khlopunov

2020

Phys. Rev. D

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“…We end by comparing the results presented here to others which have been suggested in the literature. Unlike our approach in which all results follow from first principles and in which no infinities arise, other proposals may be summarized as heuristic attempts to directly regularize point-particle self-fields [30][31][32] or expressions for the momentum associated with such fields [33]. In at least one case, the claimed force law is IR-divergent; see Eq.…”

mentioning

confidence: 99%

“…(4.4) in [30]. Other claimed force laws involve counterterms which depend on the particle's entire past history [32,33], laws which could arise only if a particle's momenta depended on its state in a highly nonlocal manner-a physically-unacceptable option. Another result predicts a time-varying mass even at lowest order [33].…”

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confidence: 99%

Self-forces on static bodies in arbitrary dimensions

2016

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We derive exact expressions for the scalar and electromagnetic self-forces and self-torques acting on arbitrary static extended bodies in arbitrary static spacetimes with any number of dimensions. Non-perturbatively, our results are identical in all dimensions. Meaningful point particle limits are quite different in different dimensions, however. These limits are defined and evaluated, resulting in simple "regularization algorithms" which can be used in concrete calculations. In these limits, self-interaction is shown to be progressively less important in higher numbers of dimensions; it generically competes in magnitude with increasingly high-order extended-body effects. Conversely, we show that self-interaction effects can be relatively large in $1+1$ and $2+1$ dimensions. Our motivations for this work are twofold: First, no previous derivation of the self-force has been provided in arbitrary dimensions, and heuristic arguments presented by different authors have resulted in conflicting conclusions. Second, the static self-force problem in arbitrary dimensions provides a valuable testbed with which to continue the development of general, non-perturbative methods in the theory of motion. Several new insights are obtained in this direction, including a significantly improved understanding of the renormalization process. We also show that there is considerable freedom to use different "effective fields" in the laws of motion---a freedom which can be exploited to optimally simplify specific problems. Different choices give rise to different inertias, gravitational forces, and electromagnetic or scalar self-forces, but there is a sense in which none of these quantities are individually accessible to experiment. Certain combinations are observable, however, and these remain invariant under all possible field redefinitions

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“…(4.4) in [47]. Other proposals use counterterms which depend on a particle's entire past history [43,48], implying that a body's momentum could not be computed without knowledge of that history-a physically-unacceptable option. Another result predicts a time-varying mass even at leading order [48].…”

Section: Comparisonsmentioning

confidence: 99%

“…Other odd-dimensional self-forces which have appeared in the literature differ much more significantly from ours. These have been obtained by the use of heuristic arguments to directly regularize point-particle self-fields [43,47], expressions for the momenta associated with those fields [48], or similar quantities. In at least one case, the claimed force law is IR-divergent; see Eq.…”

Section: Comparisonsmentioning

confidence: 99%

Foundations of the self-force problem in arbitrary dimensions

2018

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The self-force problem-which asks how self-interaction affects a body's motion-has been poorly studied for spacetime dimensions d = 4. We remedy this for all d ≥ 3 by nonperturbatively constructing momenta such that forces and torques acting on extended, self-interacting electromagnetic charges have the same functional forms as their test body counterparts. The electromagnetic field which appears in the resulting laws of motion is not however the physical one, but a certain effective surrogate which we derive. For even d ≥ 4, explicit momenta are identified such that this surrogate field satisfies the source-free Maxwell equations; laws of motion in these cases can be obtained similarly to those in the well-known four-dimensional Detweiler-Whiting prescription. For odd d, no analog of the Detweiler-Whiting prescription exists. Nevertheless, we derive its replacement. These general results are used to obtain explicit point-particle self-forces and self-torques in Minkowski spacetimes with various dimensions. Among various characteristics of the resulting equations, perhaps the most arresting is that an initially-stationary charge which is briefly kicked in 2 + 1 dimensions asymptotically returns to rest.

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Radiation reaction in 2+1 electrodynamics

Cited by 8 publications

References 21 publications

Synchrotron radiation in odd dimensions

Synchrotron radiation in odd dimensions

Self-forces on static bodies in arbitrary dimensions

Foundations of the self-force problem in arbitrary dimensions

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