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Closed-loop regularization and anomalous Ward identities

Перенормировка замкнутых петель и аномальные тождества Уорда

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Il Nuovo Cimento A (1971-1996)

Summary

Closed fermion loops with an arbitrary number of vertices are investigated by means of gauge-invariant analytic regularization. The vertices may correspond to arbitrary operators bilinear in the spinor field. A simple algorithm for the computation of these loop diagrams is presented and some useful properties are displayed. Rules for the calculation of Ward identity anomalies are given which can be executed by computer programs for Feynman diagrams. Some triangular diagrams are considered as illustrative examples.

Riassunto

Si studiano i nodi fermionici chiusi con un numero arbitrario di vertici per mezzo della regolarizzazione analitica invariante di gauge. I vertici possono corrispondere ad operatori arbitrari bilineari nel campo spinoriale. Si presenta un semplice algoritmo per il computo di questi diagrammi a nodo e si espongono alcune utili proprietà. Si danno regole per il calcolo delle anomalie dell'identità di Ward, che può essere eseguito da computer con programmi di calcolo per i diagrammi di Feynman. Si studiano come esempi illustrativi alcuni diagrammi triangolari.

Резюме

С помощью калибровочно-инвариантной аналической процедуры перенормировки исследуются замкиутые петли с произвольным числом вершин. Эти вершины могут соответствовать произвольным билинейным операторам в спинорном поле. Предлагается простой алгоритм для вычисления этих диаграмм с петлями и указываются некоторые полезные свойства. Приводятся правила для вычисления аномалий в тождехтвах Уорда, которые могут быть получены с помощяю вычислительных программ для фейнмановских диаграмм. В качестве иллюстраций рассматриваются некоторые треугольные диаграммы.

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References

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Authors and Affiliations

  1. Max-Planck-Institut für Physik und Astrophysik, München

    P. Breitenlohner

  2. Institut für Theoretische Physik, Tübingen

    H. Mitter

Authors
  1. P. Breitenlohner
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  2. H. Mitter
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Traduzione a cura della Redazione.

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Breitenlohner, P., Mitter, H. Closed-loop regularization and anomalous Ward identities. Nuov Cim A 10, 655–666 (1972). https://doi.org/10.1007/BF02899766

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  • DOI: https://doi.org/10.1007/BF02899766

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