Radiation
Reaction and Self-Force |

**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 third law does
not hold for an accelerated charge), and is associated with "radiation damping."

* __Abraham-Lorentz formula__:
An equation giving the non-relativistic form of
the self-force arising from radiation reaction,

**F**_{self} = –(4*U*/3*c*^{2})
d**v**/d*t* +
(2*e*^{2}/3*c*^{2})
d** ^{2}v**/d

where *a* is the particle's radius, and *U* the electrostatic
self-energy (which blows up as *a* → 0); It is useful in describing the motion of radiating electric charges, but it suffers from two notorious
defects, runaway solutions and preacceleration.

* __Lorentz-Dirac equation / force__:
The fully relativistic, covariant, renormalized form (in *c* = 1 units) is

*m* d*u*^{a}/d*t* = *F*_{ext}^{a}
+ (2/3)*q*^{2} (δ^{a}_{b} +
*u*^{a}*u*_{b})
d^{2}*u*^{b}/d*t*^{2} ,

where *m* includes the "electromagnetic mass" *m*_{e} = 4*U*/3*c*^{2}; > 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 d*a*^{a}/d*t* = d^{2}*u*^{a}/d*t*^{2} in
the equations introduces considerable difficulties in their interpretation as equations of motion.

* __Runaway, preaccelerated
solutions__: If *F*_{ext} =
0, a solution is **v** = **v**_{0}
+ **v**_{1} exp{*t*/*τ*},
where *τ*:= 2*e*^{2}/3*mc*^{2};
The response is that *F*_{self} applies
only when *F*_{ext} ≠ 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 dimensions;
In even *D* > 4, divergences cannot be removed by the mass renormalization

@ __Books, simple introductions__: in Panofsky & Phillips 62; in Rohrlich 65; Harte in(15)-a1405 [pedagogical introduction]; Haque EJP(14) [simple derivation].

@ __General references__: Dirac PRS(38);
Aichelburg & Beig AP(76);
Havas ln(76); Teitelboim et al RNC(80);
Higuchi qp/98 [in
quantum mechanics]; Rohrlich PRD(99)
[classical finite-size particles], AJP(00)dec
[clarification], comment Parrott gq/05;
Harpaz & Soker
IJTP(00)gq/99;
Kunze & Rendall CQG(01)gq [electromagnetism
and gravity, models]; Kozameh et al GRG(09)-a0803 [stabilized
by gravitational forces]; Gralla et al PRD(09)-a0905 [rigorous
derivation]; Poisson a0909-ln
[methods, rev]; Griffiths et al AJP(10)apr
[Abraham-Lorentz vs Landau-Lifshitz formula]; Fleming et al JPA(12)-a1106 [consistent expansion in 1/*c*, without runaways]; Polonyi AP(14) [effective dynamics]; Bender & Gianfreda JPA(15)-a1409 [PT-symmetric interpretation]; Wardell ch(15)-a1501 [approaches].

@ __Radiation reaction__: Milonni PLA(81)
[necessary for electron]; Gupta & Padmanabhan PRD(98)phy/97;
Yaremko JPS(04)#3-a0907;
Galley et al PRL(10)-a1005, comment Kazinski a1103, Galley et al PRL(12)-a1206 [finite-size correction to the Abraham-Lorentz-Dirac force]; Gal'tsov in(11)-a1012 [and energy-momentum conservation]; Yaremko & Tretyak a1207 [in classical field theory]; Yaremko JPS-a1207 [in 2+1 electrodynamics]; O'Connell CP(12) [rev]; Ilderton & Torgrimsson PLB(13)-a1301 [from QED]; Hammond FP(13) [from a scalar field]; Cabo Montes de Oca & Castiñeiras a1304; Birnholtz & Hadar PRD(14)-a1311, Birnholtz et al IJMPA(14)-a1402 [effective field theory approach]; Burton & Noble CP(14) [in strong fields]; Faci & Novello a1611, Faci et al a1706-proc [model with time delay].

@ __Preacceleration__: Valentini PRL(88);
Barut PLA(90)
[no]; Vlasov ht/97;
Villarroel PRA(97)
[1D, no]; Heras AJP(06)nov
[no], comment Jackson AJP(07)sep
+ 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]; Oliver a1306 [conceptual shift]; Deguchi et al AP-a1501 [relativistic Lagrangians]; > s.a. energy-momentum
tensor [for
relativistic
particles].

@ __In curved spacetime__: Haas a1112 [geodesics in Schwarzschild spacetime]; Kuchar et al CQG(13)-a1307 [static charge in Schwarzschild-de Sitter spacetime]; Bini et al a1610 [scalar charge orbiting a Reissner-Nordström black hole].

@
__In arbitrary dimensions__: Gal'tsov PRD(02),
Kazinski et al PRD(02)
[regularizing point-particle self-fields]; Harte et al a1708 [from first principles].

@ __Related topics__: Parrott FP(93)
[unphysical solutions, s.a. Comay FP(93)], mp/05 [Eliezer's
theorem]; de Souza BJP(98)ht/95 [and
spacetime structure]; Yaremko JMP(11) [and energy-momentum balance]; Camelio et al Chaos(12)-a1111 [and model of helium atom]; > s.a. inertia.

**In Quantum Electrodynamics** > s.a. Liénard-Wiechert
Potential; optics [optical
geometry]; QED; quantum
field theory [radiative
corrections].

@ __General references__: in Eyges 72; in Jackson 75; Vlasov phy/98;
Gill et al FP(01)phy/04 [proper
time approach]; Martin PhD(07)-a0805
[classical and quantum].

@ __Radiation damping__: Aichelburg & Beig PRD(77) [model, and cosmological
expansion]; Kunze & Rendall CQG(01)
[models, and gravity].

@ __Examples__: Vlasov ht/97-conf
[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 FP(05)gq-conf
[uniform *a* in quantum scalar field]; Medina JPA(06)phy/05 [quasi-rigid
charged body]; Rowland EJP(07)
[uniformly accelerated charge, and electromagnetic field stress-energy-momentum];
Yaremko
JPA(07)-a0907,
JMP(07)-a0907 [3D].

@ __Electrodynamics__: Ford & O'Connell PLA(91), PLA(93);
Templin AJP(98)may
[approximate]; Harpaz & Soker
IJTP(00)gq/99;
Burko
PRE(02)phy [near
dielectric]; Higuchi PRD(02)qp;
Harte PRD(06)
[extended bodies in flat spacetime]; Eriksen & Grøn PS(07)
[preradiation].

@ __In curved spacetime__: Molina & Poisson gq/05;
Galley
et al PRD(06)
[quantum field theory, and gravitational]; Sonego & Abramowicz JMP(06)gq/05 [conformally
static, optical
geometry].

**Other Fields and Topics** > s.a. energy [self-energy];
gravitational radiation reaction; origin of quantum mechanics.

@ __Acoustics__: Templin AJP(99)may
[and runaway solutions].

main page – abbreviations – journals – comments – other
sites – acknowledgements

send feedback and suggestions to bombelli at olemiss.edu – modified 16
sep 2017