Summary
We introduce the field operators characterized by the complex dimensionality parameterΔ=δ+iβ. Physical field operators, which describe scale-invariant QFT approximately, are assumed to have a definite real partδ of the dimensionality parameter and can be represented as a superposition of the operators with different values of the imaginary partβ. We show that such a formalism leads in a natural way to the introduction of nonvanishing masses and corresponding thresholds. Two-point and three-point Green’s functions are further discussed.
Riassunto
Si introducono gli operatori di campo caratterizzati dal parametro complesso di dimensionalitàΔ=δ+iβ. Si suppone che gli operatori di campo fisici, che descrivono approssimativamente la teoria quantistica dei campi invariante rispetto alla scala, abbiano una parte realeδ del parametro di dimensionalità definita, e possano essere rappresentati come sovrapposizione degli operatori con valori diversi dalla parte immaginariaβ. Si mostra come questo formalismo conduce naturalmente ad introdurre masse che non si annullano e corrispondenti valori di soglia. Poi si discutono le funzioni di Green di due e tre punti.
Реэюме
Мы вводим опрераторы поля, характериэуемые комплексным параметром многомерностиΔ=δ+iβ. Предполагается, что фиэические полевые операторы, которые приближенно описывают масщтабно-инвариант ную квантовую теорию поля, имеют определенную вешественную частьδ для параметра многомерности и могут быть представлены как суперпоэиция операторов с раэличными эначениями мнимой частиβ. Мы покаэываем, что такой формалиэм естественным обраэом приводит к введению не обрашаюшихся в нуль масс и соответствуюших порогов. Обсуждаются двухточечные и трехточечные функции Грина.
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Lukierski, J. Asymptotic logarithmic behaviour and the complex dimensionality parameter. Nuov Cim A 20, 669–677 (1974). https://doi.org/10.1007/BF02727459
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DOI: https://doi.org/10.1007/BF02727459