Summary
We consider the scalar field operator φ(x; s) describing by means of its one-particle states thes-wave stable bound states andS-wave two-particle states. The complete formulation of local quantum field theory for such field operator is presented. The generalized LSZ asymptotic condition gives the free asymptotic fields with discrete and continuous mass spectrum. The reduction formulae, defining generalized scattering amplitudes, are introduced. The unitarity condition and the notion of unstable free particle are discussed. The physical interpretation of the generalized scattering amplitudes is given.
Riassunto
Si considera l’operatore di campo scalare φ(x; s), che descrive tramite i suoi stati di una particella gli usuali stati di una particella e di due particelle dell’ondaS. Si presenta la formulazione completa della teoria quantica di campo locale per tali operatori di campo. Dalla condizione asintotica di LSZ generalizzata si hanno i campi asintotici liberi con spettro di massa discreto e continuo. Si introducono le formule di riduzione che definiscono le ampiezze di scattering generalizzate. Si discutono le condizioni di unitarietà e la nozione di particella libera instabile. Si dà l’interpretazione fisica delle ampiezze di scattering generalizzate.
Резюме
Мы рассматриваем оператор скалярного поля φ(x, s), описывающий посредством своих одно-частичных состоянийS-волновые стабильные связанные состояния иS-волновые двух-частичные состояния. Представлена полная формулировка локальной квантовой теории поля для такого полевого оператора. Обобщенное LSZ асимптотическое условие дает свободные асимптотические поля с дискретным и непрерывным массовым спектром. Вводятся рекурентные формулы, определяющие обобщенные амплитуды рассеяния. Обсуждаются условия унитарности и понятие нестабильной свободной частицы. Приводится физическая интерпретация обоб щенных амплитуд рассеяния.
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Lukierski, J. A field theory describing interacting two-particle subsystems. Nuovo Cimento A (1965-1970) 60, 353–375 (1969). https://doi.org/10.1007/BF02757009
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DOI: https://doi.org/10.1007/BF02757009