Il Nuovo Cimento A (1965-1970)

, Volume 58, Issue 2, pp 125–140 | Cite as

Local chiral symmetry for gauge theories on wilson’s lattice

  • B. F. L. Ward


With the problem of chiral symmetry on the Wilson lattice in space-time as an objective, we introduce a definition of differentiation on a lattice which respects the product rule of Leibnitz d(fg)=f dg+(df)g for functionsf, g. The derivative is essentially a generalization of the SLAC derivative on a lattice. With this derivative, chiral (symmetry) currents have all the characteristics that they possess in the continuum quantum theory of fields. In particular, the Adler-Bell-Jackiw anomaly theorem has the same form as in the continuum.

Локальная киральная симметрия для калибровочных теорий на рещетке Вильсона


При рассмотрении проблемы киральной симметрии на рещетке Вильсона в пространстве и времени мы вводим определение дифференцирования на рещетке, которое учитывает правило проиэведения Лейбница: d(fg)=f dg+(df)g для функцийf, g. Проиэводная представляет обобшение SLAC проиэводной на рещетке. Испольэуя зту проиэводную, киральные токи обладают всеми характеристиками, которые они имеют в случае непрерывной квантовой теории полей. В частности, аномальная теорема Адлера-Белла-Джакива имеет ту же форму, что и в случае континуума.


Con il problema della simmetria chirale sul reticolo di Wilson nello spazio-tempo come obbiettivo, si introduce una definizione di differenziazione sul reticolo che rispetta la regola di prodotto di Leibnitz d(fg)=f dg+(df)g per le funzionif eg. La derivata è essenzialmente una generalizzazione della derivata SLAC su di un reticolo. Con questa derivata, le correnti (di simmetrie) chirali hanno tutte le caratteristiche che possiedono nella teoria dei campi quantica nel continuo. In particolare, il teorema dell’anomalia di Adler, Bell e Jackiw ha la stessa forma che nel continuo.


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Copyright information

© Società Italiana di Fisica 1980

Authors and Affiliations

  • B. F. L. Ward
    • 1
  1. 1.Stanford Linear Accelerator CenterStanford UniversityStanford

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