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,

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); 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 dua/dt = Fexta + (2/3)q2ab + 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 equations of motion.
* Runaway, preaccelerated solutions: If Fext = 0, a solution is v = v0 + v1 exp{t/τ}, where τ:= 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 dimensions; In even D > 4, divergences cannot be removed by the mass renormalization
@ Books, simple introductions: in Panofsky & Phillips 62; in Rohrlich 65; Harte 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 a1409 [PT-symmetric interpretation]; Wardell a1501-in [approaches].
@ Radiation reaction: Milonni PLA(81) [necessary for electron]; Gupta & Padmanabhan PRD(98)phy/97; Yaremko JPS(04)#3-a0907; Galley et al a1005, comment Kazinski a1103, Galley et al PRL-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 a1301 [from QED]; Hammond FP(13) [from a scalar field]; Cabo Montes de Oca & Castiñeiras a1304; Birnholtz & Hadar a1311 [effective field theory approach]; Burton & Noble CP(14) [in strong fields].
@ 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 a1501 [relativistic Lagrangians]; > s.a. energy-momentum tensor [for relativistic particles].
@ In curved spacetime: Haas a1112 [geodesics in Schwarzschild spacetime]; Kuchar et al a1307 [static charge in Schwarzschild-de Sitter spacetime].
@ 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]; Gal'tsov PRD(02), Kazinski et al PRD(02) [any D]; Yaremko JMP(11) [and energy-momentum balance]; Camelio et al 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 pageabbreviationsjournalscommentsother sitesacknowledgements
send feedback and suggestions to bombelli at olemiss.edu – modified 8 feb 2015