Summary
The motion of a nonrelativistic extended self-interacting particle is analysed. The equation of motion is integro-differential and generates, at variance with the pointlike case, a strictly causal behaviour, thus overcoming all the fundamental shortcomings of the Abraham-Lorentz theory. The motion is endowed with memory, which generates effects totally absent in the structureless case, such as the existence of characteristic damped oscillations, whose frequency and number are determined by the specific structure.
Riassunto
Si analizza il moto di una particella non relativistica estesa autointeragente. L’equazione di moto è integrodifferenziale e genera, diversamente dal caso puntiforme, un comportamento strettamente causale, cosí superando tutti gli svantaggi fondamentali della teoria di Abraham-Lorentz. Il moto è dotato di memoria, che genera effetti totalmente assenti nel caso senza struttura, come l’esistenza di caratterestiche oscillazioni smorzate, la frequenza e il numero delle quali sono determinati dalla struttura specifica.
Резюме
Анализируется движение нерелятивистской протяженной самовзаимодействующей частицы. Уравнение движения является интегродифференциальным и, в противоречии с точечно-подобным случаем, приводит к строго причинному поведению, тем самым устраняются все основные недостатки теории Абрагама-Лоренца. Движение обладает памятью, что приводит к возникновению эффектов, полностью отсутствующих в бесструктурном случае, таких как наличие характеристических затухающих осцилляций, частота и число которых определяется специальной структурой.
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The argument goes essentially as follows. The Lamb shift for the ground state of a harmonic oscillator is, in order of magnitude,aħ 2 w 2/πmc 2; if we ascribe this energy to vibrations of the oscillator with amplitudea, so that it equalsmw 32 a 2, thena is to be interpreted as an effective radius of the electron. One getsa 2≈aħ 2/πm 2 c 2≈ƛα2 0, which is the result referred to above.
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de la Peña, L., Jiménez, J.L. & Montemayor, R. The classical motion of an extended charged particle revisited. Nuov Cim B 69, 71–88 (1982). https://doi.org/10.1007/BF02721242
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DOI: https://doi.org/10.1007/BF02721242