Generators of the exceptional group E/sub 8/ as bilinear quark and lepton fields

Journal Article · Sat Nov 14 23:00:00 EST 1981 · Phys. Rev. D; (United States)

DOI:https://doi.org/10.1103/PhysRevD.24.2636· OSTI ID:5943371

Koca, M

The quarks and leptons are assigned to the adjoint representation of the exceptional group E/sub 8/ using decompositions under the subgroups SU(9) and (SU(3))/sup 4/. Generators are constructed as linear combinations of bilinear quark and lepton fields. Closure of the algebra is used to determine the unknown coefficients of the linear combinations. It is noted that the Majorana spinors chi/sup ..mu..//sub ..nu../ introduced to represent the adjoint representations of SU(9) and (SU(3))/sup 4/ subgroups cannot be taken traceless. The trace chi/sup ..mu..//sub ..nu../ should couple to the quark and lepton fields in order to close the algebra. The constraints on the bilinear fields which are of physical importance are introduced to obtain the right number of fermionic states in the adjoint representation. An attractive possibility of having an octet of strictly massless Majorana quarks and at least three massless Majorana leptons as a consequence of pure algebraic constraints is discussed. The exceptional subgroups E/sub 7/ and E/sub 6/ are identified and the explicit commutation relations are obtained. Using one assignment of E/sub 6/ the role of color-singlet lepton-lepton and quark-antiquark currents is pointed out.

• Research Organization: Department of Theoretical Physics, University of Bielefeld, Germany
• OSTI ID: 5943371
• Journal Information: Phys. Rev. D; (United States), Journal Name: Phys. Rev. D; (United States) Vol. 24:10; ISSN PRVDA
• Country of Publication: United States
• Language: English

Related Subjects

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72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
BARYON NUMBER
COLOR MODEL
COMPOSITE MODELS
ELEMENTARY PARTICLES
FERMIONS
LEPTONS
LIE GROUPS
MAJORANA THEORY
MASSLESS PARTICLES
MATHEMATICAL MODELS
PARTICLE MODELS
POSTULATED PARTICLES
QUARK MODEL
QUARKS
SPINORS
SU GROUPS
SYMMETRY GROUPS
UNIFIED GAUGE MODELS