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On the instanton solutions for theSU 2 gauge field theory

Об инстантонных решениях дляSU 2 калибровочной теории поля

  • Published:
Il Nuovo Cimento A (1965-1970)

Summary

A new approach to the instanton solutions for theSU 2 gauge field theory is suggested. The duality condition is interpreted in terms of geometric objects and a new derivation of the number of parameters which describe a quasi-particle solution with topological indexq (≥1) is obtained. Our approach suggests that the gauge group can be interpreted as a subgroup of a larger (noncompact) Lie group. Such a picture allows us to accommodate the symmetry breaking as well as a natural introduction of the spinor fields. Finally, possibilities to extend (some of) these results to larger gauge groups are discussed.

Riassunto

Si suggerisce un nuovo approccio alle soluzioni instantoniche per la teoria di campo del gaugeSU 2. Si interpreta la condizione di dualità in termini di oggetti geometrici e si ottiene una nuova derivazione del numero di parametri che descrivono una soluzione quasi particellare con indice topologicoq (≥1). Il nostro approccio suggerisce che il gruppo di gauge sia interpretato come un sottogruppo di un gruppo di Lie più grande (non compatto). Un tale quadro ci permette di adattare la rottura di simmetria come un'introduzione naturale dei campi spinoriali. Infine si discutono le possibilità di estendere (alcuni di) questi risultati a gruppi di gauge più grandi.

Резюме

Предлагается новый подход к инстантонным решениям дляSU 2 калибровочной теории поля. Условие дуальности интерпретируется в терминах геометрических оббектов. Получается новый вывод числа параметров, которые описывают квази-частичное решение с топологическим индексомq (≥1). Наш подход предполагает, что группа калибровки может бытя интерпретирована как подгруппа большей (некомпактной) группы Ли. Такая картина позволяет рассмотреть нарушение симметрии, а также естественное введение спинорных полей. В заключение, обсуздаются возможности обобщения этих результатов на случай больших калибровочных групп.

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  1. Roon Str. 52, D-56, Wuppertal 1, Germany

    P. Tataru-Mihai

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Tataru-Mihai, P. On the instanton solutions for theSU 2 gauge field theory. Nuov Cim A 47, 287–296 (1978). https://doi.org/10.1007/BF02816547

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  • DOI: https://doi.org/10.1007/BF02816547

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