Summary
Based on the concept of a bubble electron and the approach of Pais and Uhlenbeck, we construct a finite quantum electrodynamics which is relativistically invariant, macrocausal and unitary. In this model, fields and their interaction are local, but the action function of free fields is nonlocal. The propagators are modified so that a fundamental lengthL is naturally introduced to physics. The modified static potential is given byV(r)=e/r forr>L andV(r)=0 forr<L, which is produced by the bubble sourcer −1dδ(r−L)/dr rather than by a point source. We find thatL<4·10−15 cm. Experimental consequences and modifications of strict causality at short distances |s 2|∼L 2 are discussed.
Riassunto
Basandosi sul concetto di elettrone a bolle e sull’approccio di Pais e Uhlenbeck, si costruisce una quantoelettrodinamica finita che è relativisticamente invariante, macrocausale e unitaria. In questo modello, i campi e la loro interazione sono locali, ma la funzione d’azione dei campi liberi è non locale. I propagatori sono modificati cosicchè una lunghezza fondamentaleL è naturalmente introdotta nella fisica. Il potenziale statico modificato è dato daV(r)=e/r perr>L eV(r)=0 perr<L, che è prodotto da una sorgente a bollar −1dδ(r−L)/dr piuttosto che da una sorgente puntiforme. Si trova cheL<4·10−15 cm. Si discutono le conseguenze sperimentali e le modificazioni della stretta causalità a brevi distanze, |s 2|∼L 2.
Резюме
На основе концепции пузырькового электрона и, используя подход Пейса и уленбека, мы конструируем конечную квантовую электродинамику, которая является релятивистски инвариантной, макропричинной и унитарной. В этой модели поля и взаимодействие являются локальными, но функция действия свободных полей является нелокальной. Пропагаторы модифицируются таким образом, что фундаментальная длинаL вводится естественным образом. Модифицированный статический потенциал задается следующим образомV(r)=e/r дляr>L иV(r)=0 дляr<L. Такой вид потенциала скорее дает пузырьковый источникr −1dδ(r−L)/dr, а не точечмый источник. Мы находим, чтоL<4·10−15 см. Обсуждаются экспериментальные следствия и модификации точной причинности на малых расстояниях, |s 2|∼L 2.
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Work supported in part by the U.S. ERDA.
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Hsu, J.P., Mac, E. Fundamental length, bubble electrons and nonlocal quantum electrodynamics. Nuov Cim B 49, 55–67 (1979). https://doi.org/10.1007/BF02737474
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DOI: https://doi.org/10.1007/BF02737474