Octonionic Hilbert spaces, the Poincare group and SU(3). [scalars, Poincare group, real octonions, colored states]

Journal Article · Fri Oct 01 04:00:00 EDT 1976 · J. Math. Phys. (N.Y.); (United States)

DOI:https://doi.org/10.1063/1.522811· OSTI ID:7342631

Gunaydin, M

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 Poincare 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. (AIP)

• Research Organization: Institut fur Theoretische Kernphysik der Universitat Bonn, Nussallee 14-16, D-5300 Bonn, West Germany
• OSTI ID: 7342631
• Journal Information: J. Math. Phys. (N.Y.); (United States), Journal Name: J. Math. Phys. (N.Y.); (United States) Vol. 17:10; ISSN JMAPA
• Country of Publication: United States
• Language: English

Related Subjects

645204* -- High Energy Physics-- Particle Interactions & Properties-Theoretical-- Strong Interactions & Properties
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
BANACH SPACE
COMPOSITE MODELS
ELEMENTARY PARTICLES
HADRONS
HILBERT SPACE
LIE GROUPS
MATHEMATICAL MODELS
MATHEMATICAL SPACE
PARTICLE MODELS
QUARK MODEL
SCALARS
SPACE
SU GROUPS
SU-3 GROUPS
SYMMETRY GROUPS