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Ternary symmetries and the Lorentz group

Tom 93 / 2011

Richard Kerner Banach Center Publications 93 (2011), 51-58 MSC: Primary 20C35; Secondary 20C33, 81T75, 81T05, 08A02. DOI: 10.4064/bc93-0-4

Streszczenie

We show that the Lorentz and the $SU(3)$ groups can be derived from the covariance principle conserving a $Z_3$-graded three-form on a $Z_3$-graded cubic algebra representing quarks endowed with non-standard commutation laws. The ternary commutation relations on an algebra generated by two elements lead to cubic combinations of three quarks or antiquarks that transform as Lorentz spinors, and binary quark-anti-quark combinations that transform as Lorentz vectors.

Autorzy

  • Richard KernerLPTMC, Université Pierre et Marie Curie
    CNRS URM 7600
    Tour 23
    Boîte Courrier 121
    4 Place Jussieu
    75005 Paris, France
    e-mail

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