2004
DOI: 10.1017/cbo9780511535178
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Dynamics of Charged Particles and their Radiation Field

Abstract: PrefaceBy intention, my project has two parts. The first one covers the classical electron theory. It is essentially self-contained and will be presented in the following chapters. 75 years after the discovery of quantum mechanics, to discuss only the classical version of the theory looks somewhat obsolete, in particular since many phenomena, like the stability of atoms, the existence of spectral lines and their life time, the binding of atoms, and many others, are described only by the quantized theory. Thus … Show more

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Cited by 451 publications
(666 citation statements)
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“…Hence, by (5.10) and (5.11), we have 12) which implies that W(t) * ξ ∈ D(H * ) and iW(t) * H * ξ = iH * W(t) * ξ. Therefore, we obtain (5.6).…”
Section: By This Equation and Theorem 24 (I) We Obtain (216)mentioning
confidence: 77%
“…Hence, by (5.10) and (5.11), we have 12) which implies that W(t) * ξ ∈ D(H * ) and iW(t) * H * ξ = iH * W(t) * ξ. Therefore, we obtain (5.6).…”
Section: By This Equation and Theorem 24 (I) We Obtain (216)mentioning
confidence: 77%
“…The appearance of the notoriousü term in (12) and (14) leads to pathologies such as runaway solutions and/or preacceleration which have been discussed in the literature for decades (see e.g. the texts [4,5]). An elegant (and consistent!)…”
Section: A Equations Of Motionmentioning
confidence: 99%
“…This equation was originally derived in the nonrelativistic limit by Lorentz and then generalized to the relativistic case by Abraham and Dirac [1,2,6]. It is well known that the LAD equation contains the time derivative of the acceleration of the charge (an electron, for definites) and this causes serious difficulties related to the appearance of "runaway" solutions, i. e. of solutions that show an exponential increase of the electron acceleration even in the absence of external fields (see [20,29,30,37] for a review). Dirac proposed to overcome this difficulty by postulating that the physical solutions of the LAD equation must satisfy the asymptotic condition of zeroacceleration at late times.…”
mentioning
confidence: 99%