Il Nuovo Cimento A (1965-1970)

, Volume 53, Issue 1, pp 201–212 | Cite as

Nonexistence of classes of Yang-Mills fields

  • H. G. Loos


Nonexistence is shown for regular localized free classical Yang-Mills fields with nonvanishingϕ α , with a semi-simple and compact internal holonomy group, and with one of the following types of time dependence: 1) there exists a gauge in which the potentials are independent of time, 2) the gauge fieldϕ ϰλ is covariant constant in time, 3) there exists an internal operator fieldT(x ϰ ) such that ∇ t ϕ ϰλ =[T,ϕ ϰλ ] where ∇ ϰ T belongs to the Lie algebra of the holonomy group, and the matrix formed from the adjoint representation of the gauge field and its dual has maximal rank.


Gauge Transformation Gauge Field Event Space Holonomy Group Covariant Constant 
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Отсутвие классов для полей Янга-Миллса


Показывается отсутствие для регулярных локализованных свободных классических полей Янга-Миллса с неисчезающимϕ , с полупротой и компактной внешней голономиой группой и с одним из следующих типов временной зависимости: 1) существует калибровка, в которой потенциалы не зависят от времени, 2) калибровочное полеϕ ϰλ является постоянным во времени 3) существует внешнее операторное полеT(x ϰ ), такое, что ∇ t ϕ ϰλ =[T,ϕ ϰλ , где ∇ ϰ T принадлежит алгебре Ли голономной группы, и матрица, образованная из сопряженного представления калибровочного поля и его дуала, имеет максимальный ранг.


Si dimostra la non esistenza di campi classici di Yang-Mills liberi, localizzati e regolari conϕ non nullo, con un gruppo di olonomie interne compatto e semisemplice; e con uno dei seguenti tipi di dipendenza dal tempo: 1) esiste un gauge in cui i potenziali sono indipendenti dal tempo, 2) il campo di gaugeϕ ϰλ è covariante, costante nel tempo, 3) esiste un campo interno di operatoriT(x ϰ ) tale che ∇ϕ ϰλ =[T,ϕ ϰλ , dove ∇ ϰ T appartiene all'algebra di Lie del gruppo di olonomia e la matrice formata dalla rappresentazione aggiunta del campo di gauge e del suo duale ha il massimo rango.


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Copyright information

© Società Italiana di Fisica 1968

Authors and Affiliations

  • H. G. Loos
    • 1
    • 2
  1. 1.Douglas Advanced Research LaboratoriesHuntington Beach
  2. 2.University of CaliforniaRiverside

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