Summary
We study the axial model in a background gravitational field. Using the ζ-function regularization, we obtain explicity the anomalous divergence of the axial-vector current and the exact generating functional of the theory. We show that, as a consequence of a space-time-dependent metric, all differential equations involved in the theory generalize to their covariantized forms. We also comment on the finitemass renormalization exhibited by the pseudoscalar field and the form of the fermion propagator.
Riassunto
Si studia il modello assiale in un campo gravitazionale di background. Usando la regolarizzazione della funzione ζ, si ottengono esplicitamente la divergenza anomala della corrente assiale vettoriale e l’esatta funzione generatrice della teoria. Si mostra che, in conseguenza della metrica dipendente dallo spazio tempo, tutte le equazioni differenziali coinvolte nella teoria generalizzano alla loro forma covariantizzata. Si commenta anche la rinormalizzazione di massa finita esibita dal campo pseudoscalare e la forma del propagatore fermionico.
Резюме
Мы исследуем аксиальную модель в фоновом гравитационном поле. Используя регуляризацию ζ-функции, мы получаем явно аномальную расходимость аксиально-векторного тока, и точный производящий функционал теории. Мы показываем, что, вследствие метрики, зависящей от пространства-времени, все дифференциальные уравнения, входящие в теорию, представляются в ковариантной форме. Также обсуждается конечная перенормировка массы и форма фермионного пропагатора.
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Barcelos-Neto, J., Farina, C. & Vaidya, A.N. The axial model in curved space-time. Nuovo Cim 96, 175–189 (1986). https://doi.org/10.1007/BF02721471
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DOI: https://doi.org/10.1007/BF02721471