Summary
An infinite-dimensional Lie algebraG containing the Poincaré algebra andSU 3 algebra as subalgebras is constructed. Particles with different masses can belong to the same irreducible representation ofG. A nontrivial mass formula for an octet is obtained without breaking downG. The existence of the algebraG proves that the O’Reifeartaigh’s theorem (1) cannot be generalized to denumerable infinite-dimensional Lie algebras.
Riassunto
Si costruisce un’algebra di LieG ad infinite dimensioni contenente l’algebra di Poincaré e l’algebraSU 3 come sottoalgebre. Particelle con masse differenti possono appartenere alla stessa rappresentazione irriducibile diG. Si ottiene per un ottetto una formula di massa non banale senza infrangereG. L’esistenza dell’algebraG dimostra che il teorema di O’Raifeartaigh (1) non può essere generalizzato ad algebre di Lie enumerabili ad infinite dimensioni.
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References
L. O’Raifeartaigh:Phys. Rev.,139, B 1052 (1965).
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S. Okubo andC. Ryan:Nuovo Cimento,34, 776 (1964).
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Praha 1, Myslíkova 7, Czechoslovakia.
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Formánek, J. On a mass formula without symmetry breaking. Nuovo Cimento A (1965-1970) 43, 741–751 (1966). https://doi.org/10.1007/BF02756696
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DOI: https://doi.org/10.1007/BF02756696