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A generalization of chiralSW 3 model

Обобшение чиралыюйSW 3 модели

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Il Nuovo Cimento A (1965-1970)

Summary

Assuming the algebra of currents, PCAC for pions, and some other technical conditions, we prove that any Hamiltonian densityH(x), whoseSU 3-breaking component belongs to the (3, 3*)⊕(3*, 3) representation of theSW 3-group, must automatically have the following structure:H(x)=H 0(x)+H 1(x)+H 2(x).H 0(x) is invariant underSW 3,H 1(x) breaksSU 3 but is invariant underSW 2, whileH 2(x) is invariant underSU 3 but violatesSW 2. Also,H 2(x) will vanish in the soft-pion limit. This model contains, as special cases, the schemes of Gell-Mann, Oakes and Renner, and of Glashow and Weinberg.

Riassunto

Adottando l’algebra delle correnti, la PCAC per i pioni, ed alcune altre condizioni tecniche, si dimostra che ogni densità hamiltonianaH(x), le cui componenti che infrangono la simmetria appartengono alla rappresentazione (3, 3*)⊕(3*, 3) del gruppoSW 3, deve automaticamente avere la seguente struttura:H(x)−H 0(x)+H 1(x)+H 2(x).H 0(x) è invariante rispetto aSW 3,H 1(x) infrangeSU 3 ma è invariante rispetto aSW 2, mentreH 2(x) è invariante rispetto aSU 3 ma violaSW 2. InoltreH 2(x) tende a zero nel limite del pione molle. Questo modello contiene come casi speciali gli schemi di Gell-Mann, Oakes e Rennes, e di Glashow e Weinberg.

Реэюме

Предполагая алгебру токов, РСАС для пионов и некоторые другие технические условия, докаэывается, что любая плотность ГамильтонианаH (x) чья компонента, нарущаюшаяSU 3, принадлежит (3, 3*)⊕(3*, 3) представлению группыSW 3, должна автоматически иметь следуюшую структуру:H(x)=H 0(x)++H 1(x)+H 2(x).H 0(x) является инвариантным относительноSW 3,H 1(x) нарущаетSU 3, но является инвариантным относительноSW 2, тогда какH 2(x) инвариантно относительноSU 3, но нарущаетSW 2. Кроме того,H 2(x) обрашается в нуль в пределе мягких пионов. Эта модель содержит, как честные случаи, схемы Гелл-Мана, Оакса и Реннера, и Глащоу и Вейнберга.

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Authors and Affiliations

  1. Department of Physics and Astronomy, University of Rochester, Rochester, N.Y.

    S. Okubo

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To speed up publication, the author of this paper has agreed to not receive the proofs for correction.

Work supported in part by the U.S. Atomic Energy Commission.

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Okubo, S. A generalization of chiralSW 3 model. Nuov Cim A 7, 765–778 (1972). https://doi.org/10.1007/BF02728809

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