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Il Nuovo Cimento A (1965-1970)

, Volume 11, Issue 2, pp 397–435 | Cite as

A renormalizable gauge model of lepton interactions

  • Abdus Salam
  • J. Strathdee
Article

Summary

It is known that the spontaneous violation of a gauge symmetry of the second kind results in the appearance not of Goldstone bosons but, rather, of massive gauge particles. The path-integral quantization of these theories is discussed here in general terms. The primary consideration is that quantities of physical significance, such as matrix elements of the scattering operator or the energy-momentum tensor, should be independent of the gauge in which the quantization rules are formulated. In particular, if it is possible to find one gauge in which the theory is unitary and another in which it is renormalizable, then the gauge-independent quantities must enjoy both these qualities. These ideas are applied to simple models with massive Yang-Mills fields and to a model which unifies the weak and electromagnetic interactions of electron-type leptons. Both these models appear to be unitary and renormalizable. The lepton theory is a relatively economical one. It involves five independent parameters: the electron charge and mass, the mass of the charged intermediate vector boson and the masses of a neutral scalar and a neutral vector boson.

Перенормируемая калибровочная модель лептонных вэаимодействий

Реэюме

Иэвестно, что спонтанное нарущение калибровочной симметрии второго рода приводит к появлению не боэонов Голдстоуна, а скорее массивных калибровочных частиц. В зтой работе в обших выражениях обсуждается квантование с помошью контурных интегралов таких теорий. Исходное соображение состоит в том, что величины, имеюшие фиэический смысл, такие как матричные злементы оператора рассеяния или тенэор знергии-импульса, должны быть не эависимыми от калибровки, в которой формулируются правила квантования. В частности, если воэможно найти одну калибровку, в которой теория является унитарной, и другую калибровку, в которой теория является перенормируемой, тогда не эависяшие от калибровки величины должны обладать обоими качествами. Эти идеи применяются к простой модели с массивными полями Янга-Миллса и к модели, которая общединяет слабые и злектромагнитные вэаимодействия лептонов злектронного типа. Обе зти модели окаэываются унитарными и перенормируемыми. Лептонная теория является относительной зкономной. Эта теория включает пять неэависимых параметров: эаряд и массу злектрона, массу эаряженного промежуточного векторного боэона и массы нейтрального скалярного и нейтрального векторного боэонов.

Riassunto

È noto che la violazione spontanea di una simmetria di gauge di seconda specie produce l’apparizione non di bosoni di Goldstone ma, piuttosto, di particelle di gauge con massa. Si discute qui in termini generali la quantizzazione dell’integrale di percorso di queste teorie. La considerazione primaria è che le grandezze di significato fisico, como gli elementi di matrice dell’operatore di scattering o il tensore energia-impulso, devono essere indipendenti dal gauge in cui si formulano le regole di quantizzazione. In particolare, se è possible trovare un gauge in cui la teoria è unitaria ed un altro in cui essa è rinormalizzabile, allora le grandezze indipendenti dal gauge devono godere di entrambe queste qualità. Si applicano queste idee ad un semplice modello con campi di Yang-Mills con massa e ad un modello che unifica le interazioni deboli ed elettromagnetiche dei leptoni del tipo dell’elettrone. Entrambi questi modelli risultano unitari e rinormalizzabili. La teoria del leptone è relativamente economica. Essa comporta cinque parametri indipendenti: la massa e la carica dell’elettrone, la massa del bosone vettoriale intermedio carico, e le masse di un bosone scalare neutro e di un bosone vettoriale neutro.

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References

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Copyright information

© Società Italiana di Fisica 1972

Authors and Affiliations

  • Abdus Salam
    • 1
    • 2
  • J. Strathdee
    • 3
  1. 1.International Centre for Theoretical PhysicsTrieste
  2. 2.Imperial CollegeLondon
  3. 3.International Centre for Theoretical PhysicsTrieste

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