Summary
Generalization of the Goldstone theorem and of the Coleman theorems are formulated and proven within the framework of the Wightman field theory. The generalization of the Goldstone theorem is to a class of currents in which implicit and explicit co-ordinate dependence are mixed. We get that vacuum noninvariance entails the existence of certain masses in the energy-momentum spectrum which are not necessarily zero. The generalizations of the Coleman theorems are to local tensor fields and to several classes of fields in which implicit and explicit co-ordinate dependence are mixed. Several examples are examined in light of the new theorems.
Riassunto
Si formulano generalizzazioni del teorema di Goldstone e dei teoremi di Coleman e le si dimostra nel contesto della teoria dei campi di Wightman. Si generalizza il teorema di Goldstone ad una classe di correnti in cui le dipendenze implicita ed esplicita delle coordinate sono mescolate. Si ottiene che la non invarianza del vuoto comporta l’esistenza di alcune masse nello spettro dell’energia-impulso che non sono necessariamente nulle. I teoremi di Coleman si generalizzano a campi tensoriali locali ed a numerose classi di campi in cui le dipendenze implicita ed esplicita dalle coordinate sono mescolate. Si esaminano numerosi esempi alla luce dei nuovi teoremi.
Реэуме
Формулируутся и докаэываутся обобшения теоремы Голдстоуна и теорем Колемана в рамках теории поля Ваитмана. Теорема Голдстоуна обобшается на класс токов, в котором перемещиваутся неявная и явная эависимости от координат. Мы получаем, что неинвариантностя вакуума приводит к сушествованиу некоторых масс в спектре знергии-импуляса, которые не являутся обяэателяно нулями. Теоремы Колемана обобшаутся на локаляные тенэорные поля и некоторые классы полеи, в которых перемещиваутся неявная и явная эависимости от координат. Исследуутся некоторые примеры в свете зтих новых теорем.
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Dothan, Y., Gal-Ezer, E. Generalizations of the goldstone and the coleman theorems. Nuov Cim A 12, 465–479 (1972). https://doi.org/10.1007/BF02729558
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DOI: https://doi.org/10.1007/BF02729558