Summary
It is demonstrated that the apparent breakdown of Lorentz invariance in current-current interaction theories may be resolved, at least to lowest order in the coupling, by altering the definition of the currentj μ. This is accomplished by multiplying the naive definition by an exponential factor,\(\left[ {i\lambda \int\limits_{\alpha - s}^{\alpha + s} {d\varphi ^\nu j_\nu \left( \varphi \right)} } \right]\), and proving the theory to be consistent with Lorentz invariance to lowest order in a Taylor-series expansion of the exponential. Possible effects due to higher-order terms in the exponential are briefly mentioned, including the possibility of their affecting the validity of the CVC and PCAC theorems.
Riassunto
Si dimostra che l’apparente rottura dell’invarianza di Lorentz nelle teorie dell’interazione corrente-corrente può essere risolta, almeno al più basso ordine nell’accoppiamento, alterando la definizione della correntej μ. Questo si realizza moltiplicando la semplice definizione per un fattore esponenziale,\(\left[ {i\lambda \int\limits_{\alpha - s}^{\alpha + s} {d\varphi ^\nu j_\nu \left( \varphi \right)} } \right]\), e provando che la teoria è coerente con l’invarianza di Lorentz al più basso ordine nello sviluppo dell’esponenziale in serie di Taylor. Si citano brevemente possibili effetti dovuti a termini di ordine maggiore nell’esponenziale, includendo la possibilità che essi influiscano sulla validità dei georemi di CVC e PCAC.
Резюме
Демонстрируется, что кажущееся нарушение Лорентц-инвариан-тности в теориях ток-токовых взаимодействий может быть разрешено, по крайней мере, в ниешем порядке по связи, посредством изменения определения токаj μ. Это достигается путем умножения обычного определения на экспоненциальный множитель\(\left[ {i\lambda \int\limits_{\alpha - s}^{\alpha + s} {d\varphi ^\nu j_\nu \left( \varphi \right)} } \right]\), и доказывается, что эта теория не противоречит Лорентц-инвариантности в низшем порядке при разложении экспоненты в ряд тейлора. Вкратце отмечаются возможные эффекты, обусловленные членами более более высокого порядка в экспоненте, включая возможность их влияния на справедливость теорем CVC и PCAC.
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Research supported by the Atomic Energy Commission and AFOSR, Grant Number AF-AFOSR 1296-67.
Traduzione a cura della Redazione.
Перевебено ребакуией.
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Cohen, S.L. Current definitions and Schwinger terms. Nuovo Cimento A (1965-1970) 62, 881–888 (1969). https://doi.org/10.1007/BF02818755
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DOI: https://doi.org/10.1007/BF02818755