Summary
A distinction between two types of spontaneous sym metry breakings is made: “asymptotical” breaking and “local” breaking. The former is characterized by a conserved symmetry current and by the presence of Goldstone bosons (or long-range interactions), and occurs in the BCS-theory as well as in classical theories. For local breakings the usual proof of current conservation breaks down as a result of the singularity of a product of field operators at one point, as occurring in currents and their divergences. This case is realized in certain local quantum field theories,e.g. in quantum electrodynamics with zero bare mass. Local breakings, in contradistinction to asymptotical ones, might be useful in a field theory of elementary particles.
Riassunto
Si distingue fra due tipi di rottura spontanea della simmetria: quella “asintotica” e quella “locale”. La prima è caratterizata da una corrente di simmetria conservata e dalla presenza di bosoni di Goldstone (oppure di interazioni a lungo raggio), e si verifica tanto nella teoria di BCS che in quella classica. Per le rotture locali la consueta prova di conservazione della corrente viene meno come risultato della singolarità del proclotto degli operatori di campo in un punto, come accade nelle correnti e le loro divergenze. Questo caso si verifica in alcune teorie di campo locale quantizzato, per esempio l’elettrodinamica quantistica con massa nuda nulla. Le rotture locali, contrariamente a quelle asintotiche, possono essere utilizzate in una teoria di campo per le particelle elementari.
Резюме
Делается различие между двумя типами спонтанного нарушения симметрии: “асимптотическое” нарушение и “локальное” нарушение. Первый тип характеризуется сохраняющимся симметричным током и наличием бозонов Голдстоуна (или дальнодействующими взаимодействиями) и встречается в BCS-теории так же, как и в классических теориях. Для локальных нарушений обычное доказательство сохранения тока нарушается как результат синтулярности произведения операторов поля в одной точке, встречающееся в токах и их производных. Этот случай реализуется в локальных квантовых теориях поля, т.е. в квантовых электродинамиках с нулевой затравочной массой. Локальные нарушения, в отличие от асимптотических нарушений, могут быть использованы в теории поля элементарных частиц.
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Maris, T.A.J., Jacob, G. & Liberman, B. Two ways of spontaneous symmetry breaking. Nuovo Cimento A (1965-1970) 52, 116–121 (1967). https://doi.org/10.1007/BF02739278
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DOI: https://doi.org/10.1007/BF02739278