Fundamental Fermions Fit Inside One <Emphasis Type="Italic">su</Emphasis>(1|5) Irreducible Representation |
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Authors: | Email author" target="_blank">N?I?StoilovaEmail author J?Van?der?Jeugt |
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Institution: | (1) Department of Applied Mathematics and Computer Science, University of Ghent, Krijgslaan 281-S9, Gent, Belgium, B-9000;(2) Institute for Nuclear Research and Nuclear Energy, Boul. Tsarigradsko Chaussee 72, 1784 Sofia, Bulgaria |
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Abstract: | The Lie superalgebra su(1|5) has irreducible representations of dimension 32, in which the 32 fundamental fermions of one generation (leptons and
quarks, of left and right chirality, and their antiparticles) can be accommodated. The branching of these su(1|5) representations with respect to its subalgebra su(3)× su(2)× u(1) reproduces precisely the classification of these fundamental fermions according to the gauge group su(3)c× su(2)w× u(1)w of the Standard Model. Furthermore, a simple construction of the relevant representations is given, and some consequences
are discussed. |
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Keywords: | gauge theories unified theories group theoretical models classification of fundamental fermions Lie superalgebra su(1|5) |
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