Octonionic Hilbert Spaces, the Poincare Group and SU(3)

Gunaydin, Murat

doi:10.1063/1.522811

Octonionic Hilbert Spaces, the Poincare Group and SU(3)

Murat Gunaydin
(
- Bonn U.
)

Feb, 1976

39 pages

Published in:

J.Math.Phys. 17 (1976) 1875

DOI:

10.1063/1.522811

Report number:

Print-76-0125 (BONN)

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Abstract: (AIP)

A formalism based on real octonions is developed in order to construct an octonionic Hilbert space for the description of colored quark states. The various possible forms of scalar products and related scalars are discussed. The choice of a direction in the space of octonion units leads naturally to a representation of the Poincaré group in terms of complex scalar products and complex scalars. The remaining octonion directions span the color degrees of freedom for quarks and anti‐quarks. In such a Hilbert space, product states associated with color singlets are shown to form a physical quantum mechanical Hilbert space for the description of hadrons. Color triplets, on the other hand, correspond to unobservable parafermion states of order three.

linear space: HILBERT SPACE
GROUP THEORY: LORENTZ
SYMMETRY: SU(3)
QUARK: COLOR
MODEL: TRIPLET
FERMION: PARAFERMION
QUARK: STATISTICS

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Figures(0)

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