Quaternion-Octonion SU(3) Flavor Symmetry
Pushpa, P. S. Bisht, Tianjun Li, O. P. S. Negi
TL;DR
This paper extends quaternionic and octonionic formalisms to SU(3) flavor symmetry, deriving new relations and commutation rules for quark states and isospin multiplets using octonion variables.
Contribution
It introduces a novel octonion-based approach to SU(3) flavor symmetry, deriving and verifying new commutation relations for the group and its multiplets.
Findings
Derived relations for isospin components with quark states.
Reconsidered octonion splitting of SU(3) group.
Verified commutation relations for iso-spin multiplets.
Abstract
Starting with the quaternionic formulation of isospin SU(2) group, we have derived the relations for different components of isospin with quark states. Extending this formalism to the case of SU(3) group we have considered the theory of octonion variables. Accordingly, the octonion splitting of SU(3) group have been reconsidered and various commutation relations for SU(3) group and its shift operators are also derived and verified for different iso-spin multiplets i.e. I, U and V- spins. Keywords: SU(3), Quaternions, Octonions and Gell Mann matrices PACS NO: 11.30.Hv: Flavor symmetries; 12.10-Dm: Unified field theories and models of strong and electroweak interactions
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