Quaternion-Octonion SU(3) Flavor Symmetry

  title={Quaternion-Octonion SU(3) Flavor Symmetry},
  author={Pushpa and P. S. Bisht and Tianjun Li and O. P. S. Negi},
  journal={International Journal of Theoretical Physics},
  • Pushpa, P. Bisht, O. Negi
  • Published 8 July 2011
  • Physics
  • International Journal of Theoretical Physics
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 isospin multiplets i.e. I, U and V-spins. 
Quaternion-Octonion Unitary Symmetries and Analogous Casimir Operators
An attempt has been made to investigate the global SU(2) and SU(3) unitary flavor symmetries systematically in terms of quaternion and octonion respectively. It is shown that these symmetries are
Quaternion-Octonion Unitary Symmetries and Analogous
An attempt has been made to investigate the global SU(2) and SU(3) unitary flavor symmetries systematically in terms of quaternion and octonion respectively. It is shown that these symmetries are
Octonion and Split Octonion Representation of SO(8) Symmetry
The 8 $\times$ 8 matrix representation of SO(8) Symmetry has been defined by using the direct product of Pauli matrices and Gamma matrices. These 8 $\times$ 8 matrices are being used to describe the
Generalised Split Octonions and Their Transformation in SO(7) Symmetry
Generators of $\operatorname{SO}(8)$ group have been described by using direct product of the Gamma matrices and the Pauli Sigma matrices. We have obtained these generators in terms of generalized
On octonion quark confinement condition
The octonion algebra is analyzed using a formalism that demonstrates its use in color quark confinement. In this study, we attempt to write a connection between octonion algebra and SU(3)[Formula:
Role of division algebra in seven-dimensional gauge theory
The algebra of octonions 𝕆 forms the largest normed division algebra over the real numbers ℝ, complex numbers ℂ and quaternions ℍ. The usual three-dimensional vector product is given by quaternions,
Reconstruction of symmetric Dirac-Maxwell equations using nonassociative algebra
In the presence of sources, the usual Maxwell equations are neither symmetric nor invariant with respect to the duality transformation between electric and magnetic fields. Dirac proposed the


Quaternion Octonion Reformulation of Quantum Chromodynamics
We have made an attempt to develop the quaternionic formulation of Yang–Mill’s field equations and octonion reformulation of quantum chromo dynamics (QCD). Starting with the Lagrangian density, we
Quark structure and octonions
The octonion (Cayley) algebra is studied in a split basis by means of a formalism that brings outs its quarkstructure. The groups SO(8), SO(7), and G 2 are represented by octonions as well as by 8 ×
Gauge Theories over Quaternionsand Weinberg-Salam Theory
The left-right symmetric Weinberg-Salam theory with SU(2)LXSU(2lRx UO) is re formulated as a quaternionic gauge theory. It is argued that the concept of generation favors quaternions. quaternionic
On the noncommutative and nonassociative geometry of octonionic space time, modified dispersion relations and grand unification
The octonionic geometry (gravity) developed long ago by Oliveira and Marques, J. Math. Phys. 26, 3131 (1985) is extended to noncommutative and nonassociative space time coordinates associated with
Towards an algebraic quantum chromodynamics
We outline a quantum theory of quarks and gluons based on fields with values taken from a noncommutative Jordan algebra. These fields automatically satisfy a triality rule: Quark-antiquark and
An extension of quaternionic metrics to octonions
A treatment of a non‐Riemannian geometry including internal complex, quaternionic, and octonionic space is made. Then, an interpretation of this geometry for the nonsymmetric theory of
Lie Algebras in Particle Physics
Howard Georgi is the co-inventor (with Sheldon Glashow) of the SU(5) theory. This extensively revised and updated edition of his classic text makes the theory of Lie groups accessible to graduate
The Lie algebras su(N)
Square Hermitian matrices and their basis elements are displayed. The traceless version is formed. Square anti-Hermitian matrices are shown to constitute a Lie algebra(u(N)).The traceless version
Geometrical properties of an internal local octonionic space in curved space-time.
A geometrical treatment on a flat tangent space local to a generalized complex, quaternionic, and octonionic space-time is constructed. It is shown that it is possible to find an
The Lie Algebras Su(n): An Introduction
1 Lie algebras.- 1.1 Definition and basic properties.- 1.1.1 What is a Lie algebra?.- 1.1.2 The structure constants.- 1.1.3 The adjoint matrices.- 1.1.4 The Killing form.- 1.1.5 Simplicity.- 1.1.6