Summary
The problem of the decay of an unstable elementary particle is analysed from the point of view of a quantum-mechanical theory of randomly repeated measurements. A semi-group law of evolution, on the space of all density matrices, is shown to result. This situation is contrasted with some earlier work on the problem where a semi-group law of evolution on a Hilbert space of state vectors was postulated. Many of the difficulties of this older theory are naturally resolved within the context of the currently proposed theory.
Riassunto
Il problema del decadimento di una particella elementare instabile è analizzato nello spirito di una teoria quantistica che include il verificarsi di processi di misura ripetuti, a tempi a caso. Si mostra che ne consegue una legge di evoluzione a semi-gruppo nello spazio delle matrici densità. Questa situazione è in contrapposizione con alcuni lavori precedenti sul medesimo problema, nei quali la legge di evoluzione a semi-gruppo era assunta valere nello spazio di Hilbert dei vettori di stato. Molte difficoltà di queste teorie sono risolte in modo naturale nel contesto della teoria qui proposta.
Реэюме
Аналиэируется проблема распада нестабильной злементарной частицы, исходя иэ квантовомеханическ ой теории случайно повторяюшихся иэмерений. Иэ аналиэа вытекает полугрупповой эакон зволюции на простванстве всех матриц плотности. Укаэанная ситуация контрастирует с предыдушей работой, касаюшейся зтой проблемы, в которой постулируется полугрупповой эакон зволюции на гильбертовом пространстве векторов состояний. В рамках предложенной теории естественным обраэом раэрещаются многие трудности предыдушей теории.
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Supported in part by the Istituto Nazionale di Fisica Nucleare, Sezione di Trieste.
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Twareque Ali, S., Fonda, L. & Ghirardi, G.C. Pertinence of the semi-group law in the theory of the decay of an unstable elementary particle. Nuov Cim A 25, 134–148 (1975). https://doi.org/10.1007/BF02735615
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DOI: https://doi.org/10.1007/BF02735615