In General > s.a. electromagnetism;
classical particles;
particle effects; QED.
* Radiation reaction:
The effect on a radiation-emitting particle due to the fact that energy, momentum
and
angular
momentum are carried
away by the radiation;
It can
be described in terms of a "self-force" (Newton's 3rd law does not
hold for an accelerated charge), and is associated with "radiation damping."
* Abraham-Lorentz formula: Describes the non-relativistic form of
the self-force arising from radiation reaction,
Fself = –(4U/3c2) dv/dt + (2e2/3c2) d2v/dt2 + O(a) ,
where a is the particle's radius, and U the electrostatic self-energy
(blows up as a → 0).
* Lorentz-Dirac equation/force:
The fully relativistic, covariant, renormalized form (c = 1)
m dua/dt = Fexta
+ (2/3)q2 (
ab +
uaub)
d2ub/dt2 ,
where m includes the "electromagnetic mass" me = 4U/3c2; > s.a.
mass.
* Eliezer's theorem:
An electron moving radially according to the Lorentz-Dirac equation in the
Coulomb
field
of a proton will not be
attracted to a collision with the proton; Instead, it is repelled
from the proton with proper acceleration increasing asymptotically with proper
time; Proponents of the Lorentz-Dirac equation sometimes try to explain this
away by speculation that the electron must approach so closely to the proton
that the field strength would be beyond the domain of validity of the classical
Lorentz-Dirac equation and therefore require a quantum-mechanical analysis,
but this explanation does not seem to hold.
* Issue: The presence
of daa/dt = d2ua/dt2 in
the equations introduces considerable difficulties in their interpretation
as eom's.
* Runaway, preaccelerated
solutions: If Fext =
0, a solution is v = v0 + v1
exp{t/
},
where
:=
2e2/3mc2;
The response is that Fself applies
only when Fext
0
and the energy
loss is small; Confirmed by QED.
* In other dimensions:
(Gal'tsov) Radiation reaction allows a consistent mass renormalization
only in 4D; In odd dimensions Huygens's principle does not
hold and the radiation reaction force depends on the whole past
history of the charge (radiative tail), with a divergence in the
tail integral that can be removed by mass renormalization only in (2+1)-D;
In even D > 4, divergences cannot be removed by the
mass
renormalization
@ General references: Dirac PRS(38);
in Panofsky & Phillips 62; in Rohrlich
65; Aichelburg & Beig AP(76);
Havas ln(76); Teitelboim et al RNC(80);
Higuchi qp/98 [in
qm]; Rohrlich PRD(99)
[classical finite-size particles], AJP(00)
[clarification], comm Parrott gq/05/PRD;
Harpaz & Soker
IJTP(00)gq/99;
Kunze & Rendall CQG(01)gq [em
and gravity, models].
@ Radiation reaction: Milonni PLA(81) [necessary for electron].
@ Preacceleration: Valentini PRL(88);
Barut PLA(90)
[no]; Vlasov ht/97;
Villarroel PRA(97)
[1D, no]; Heras AJP(06)
[no], comment Jackson AJP(07)
+ Hnizdo + reply; Jiménez et al FP(06)
[model].
@ Lorentz-Dirac equation: Vlasov ht/97 [instability];
Sonego JMP(99)
[conformal behavior]; Poisson gq/99 [intro];
Chicone et al PLA(01)gq [delay
equations and bifurcations]; Rohrlich PLA(01)
[criticism], PLA(02)
[quasi-point charges];
Yaremko JPA(02);
Hussein et al MPLA(02)
[causal integration]; O'Connell
PLA(03)qp;
Higuchi & Martin PRD(04)qp [from
QED]; Aguirregabiria et al PRD(06)
[modified, less restrictive assumptions]; > s.a. energy-momentum [for
relativistic
particles].
@ Related topics: Parrott FP(93)
[unphysical solutions, s.a. Comay FP(93)], mp/05 [Eliezer's
theorem]; de Souza BJP(98)ht/95 [and
st structure]; Gal'tsov PRD(02),
Kazinski et al PRD(02)
[any D].
In (Quantum) Electrodynamics > s.a. Liénard-Wiechert
Potential; optics [optical
geometry]; QED; qft [radiative
corrections].
@ General references: in Eyges 72; in Jackson 75; Vlasov phy/98; Gill et al FP(01)phy/04 [proper
time approach].
@ Radiation damping: Aichelburg & Beig PRD(77) [model, and cosmological
expansion]; Kunze & Rendall CQG(01)
[models, and gravity].
@ Examples: Vlasov ht/97-in
[1D extended particle], phy/97 [rigid
charged body], phy/98 [rotating
charged sphere]; Unruh PRA(99)
[accelerated dipole];
Higuchi
& Martin FP(05)qp [linear
acceleration]; Johnson & Hu gq/05-in
[uniform a in quantum scalar field]; Medina JPA(06)phy/05 [quasi-rigid
charged body]; Rowland EJP(07)
[uniformly accelerated charge, and em field stress-energy-momentum]; Yaremko
JPA(07),
JMP(07)
[3D].
@ Electrodynamics: Ford & O'Connell PLA(91), PLA(93);
Templin AJP(98)
[approximate]; Harpaz & Soker
IJTP(00)gq/99;
Burko
PRE(02)phy [near
dielectric]; Higuchi PRD(02)qp;
Harte PRD(06)
[extended bodies in flat st]; Eriksen & Grøn PS(07)
[preradiation].
@ In curved spacetime: Molina & Poisson gq/05;
Galley
et al PRD(06)
[qft, and gravitational]; Sonego & Abramowicz JMP(06)
[conformally static, optical
geometry].
Other Fields and Topics > s.a. energy [self-energy];
gravitational radiation reaction.
@ Acoustics: Templin AJP(99) [and runaway solutions].
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Send feedback and suggestions to bombelli at olemiss.edu – Modified
27 apr 2008