Quaternionic approach to dual Magneto-hydrodynamics of dyonic cold plasma

The dual magneto-hydrodynamics of dyonic plasma describes the study of electrodynamics equations along with the transport equations in the presence of electrons and magnetic monopoles. In this paper, we formulate the quaternionic dual fields equations, namely, the hydro-electric and hydro-magnetic fields equations which are an analogous to the generalized Lamb vector field and vorticity field equations of dyonic cold plasma fluid. Further, we derive the quaternionic Dirac-Maxwell equations for dual magneto-hydrodynamics of dyonic cold plasma. We also obtain the quaternionic dual continuity equations that describe the transport of dyonic fluid. Finally, we establish an analogy of Alfven wave equation which may generate from the flow of magnetic monopoles in the dyonic field of cold plasma. The present quaternionic formulation for dyonic cold plasma is well invariant under the duality, Lorentz and CPT transformations.Comment: 20 pages, Revised versio

On the quaternion transformation and field equations in curved space-time

In this paper, we use four-dimensional quaternionic algebra to describing space-time field equations in curvature form. The transformation relations of a quaternionic variable are established with the help of basis transformations of quaternion algebra. We deduced the quaternionic covariant derivative that explains how the quaternion components vary with scalar and vector fields.The quaternionic metric tensor and geodesic equation are also discussed to describing the quaternionic line element in curved space-time. Moreover, we discussed an expression for the Riemannian Christoffel curvature tensor in terms of the quaternionic metric tensor. We have deduced the quaternionic form of Einstein-field-like equation which shows an equivalence between quaternionic matter and geometry.Comment: 22 page

Z_2 Graded Lie Algebra of Quaternions and Superconformal Algebra in D=4 dimensions

In the present discussion, we have studied the Z2-grading of quaternion algebra (H). We have made an attempt to extend the quaternion Lie algebra to the graded Lie algebra by using the matrix representations of quaternion units. The generalized Jacobi identities of Z2-graded algebra then result in symmetric graded partners (N1;N2;N3). The graded partner algebra (F) of quaternions (H) thus has been constructed from this complete set of graded partner units (N1;N2;N3), and N0 = C. Keeping in view the algebraic properties of the graded partner algebra (F), the Z2-graded superspace (Sl;m) of quaternion algebra (H) has been constructed. It has been shown that the antiunitary quaternionic supergroup UUa(l;m;H) describes the isometries of Z2-graded superspace (Sl;m). The Superconformal algebra in D = 4 dimensions is then established, where the bosonic sector of the Superconformal algebra has been constructed from the quaternion algebra (H) and the fermionic sector from the graded partner algebra (F).Comment: 23 page

Octonion Quantum Chromodynamics

Starting with the usual definitions of octonions, an attempt has been made to establish the relations between octonion basis elements and Gell-Mann \lambda matrices of SU(3)symmetry on comparing the multiplication tables for Gell-Mann \lambda matrices of SU(3)symmetry and octonion basis elements. Consequently, the quantum chromo dynamics (QCD) has been reformulated and it is shown that the theory of strong interactions could be explained better in terms of non-associative octonion algebra. Further, the octonion automorphism group SU(3) has been suitably handled with split basis of octonion algebra showing that the SU(3)_{C}gauge theory of colored quarks carries two real gauge fields which are responsible for the existence of two gauge potentials respectively associated with electric charge and magnetic monopole and supports well the idea that the colored quarks are dyons