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Split Octonion Electrodynamics and EnergyMomentum Conservation Laws for Dyons” (Communicated
, 2012
"... Starting with the usual definations of octonions and split octonions in terms of Zorn vector matrix realization, we have made an attempt to write the consistent form of generalized Maxwell’s equations in presence of electric and magnetic charges. We have thus written the generalized split octonion p ..."
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Starting with the usual definations of octonions and split octonions in terms of Zorn vector matrix realization, we have made an attempt to write the consistent form of generalized Maxwell’s equations in presence of electric and magnetic charges. We have thus written the generalized split octonion potential wave equations and the generalized fields equation of dyons in split octonions. Accordingly the split octonion forms of generalized Dirac Maxwell’s equations are obtained in compact and consistent manner. Accordingly, we have made an attempt to investigate the work energy theorem or “Poynting Theorem”, Maxwell stress tensor and Lorentz invariant for generalized fields of dyons in split octonion electrodynamics. Our theory of dyons in split octonion formulations is discussed in term of simple and compact notations. This theory reproduces the dynamic of electric (magnetic) in the absence of magnetic (electric) charges. 1
Conformal Gravity, Maxwell and YangMills Unification in 4D from a Clifford Gauge Field Theory
, 2009
"... A model of Emergent Gravity with the observed Cosmological Constant from a BFChernSimonsHiggs Model is revisited which allows to show how a Conformal Gravity, Maxwell and SU(2) × SU(2) × U(1) × U(1) YangMills Unification model in four dimensions can be attained from a Clifford Gauge Field The ..."
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A model of Emergent Gravity with the observed Cosmological Constant from a BFChernSimonsHiggs Model is revisited which allows to show how a Conformal Gravity, Maxwell and SU(2) × SU(2) × U(1) × U(1) YangMills Unification model in four dimensions can be attained from a Clifford Gauge Field Theory in a very natural and geometric fashion.
PA ijpam.eu GEOMETRICAL WAVE EQUATION AND THE CAUCHYLIKE THEOREM FOR OCTONIONS
"... Abstract: Riemann surfaces, cohomology and homology groups, Cartan’s spinors and triality, octonionic projective geometry, are all well supported by Complex Structures [1], [2], [3], [4]. Furthermore, in Theoretical Physics, mainly in General Relativity, Supersymmetry and Particle Physics, Complex T ..."
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Abstract: Riemann surfaces, cohomology and homology groups, Cartan’s spinors and triality, octonionic projective geometry, are all well supported by Complex Structures [1], [2], [3], [4]. Furthermore, in Theoretical Physics, mainly in General Relativity, Supersymmetry and Particle Physics, Complex Theory Plays a Key Role [5], [6], [7], [8]. In this context it is expected that generalizations of concepts and main results from the Classical Complex Theory, like conformal and quasiconformal mappings [9], [10] in both quaternionic and octonionic algebra, may be useful for other fields of research, as for graphical computing enviromment [11]. In this Note, following recent works by the autors [12], [13], the Cauchy Theorem will be extended for Octonions in an analogous way that it has recentely been made for quaternions [14]. Finally, will be given an octonionic treatment of the wave equation, which means a wave produced by a hyperstring with initial conditions similar to the onedimensional case.
THE EXCEPTIONAL E8 GEOMETRY OF CLIFFORD (16) SUPERSPACE AND CONFORMAL GRAVITY YANG–MILLS GRAND UNIFICATION
, 2008
"... We continue to study the Chern–Simons E8 Gauge theory of Gravity developed by the author which is a unified field theory (at the Planck scale) of a Lanczos–Lovelock Gravitational theory with a E8 Generalized Yang–Mills (GYM) field theory, and is defined in the 15D boundary of a 16D bulk space. The E ..."
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We continue to study the Chern–Simons E8 Gauge theory of Gravity developed by the author which is a unified field theory (at the Planck scale) of a Lanczos–Lovelock Gravitational theory with a E8 Generalized Yang–Mills (GYM) field theory, and is defined in the 15D boundary of a 16D bulk space. The Exceptional E8 Geometry of the 256dim slice of the 256 × 256dimensional flat Clifford (16) space is explicitly constructed based on a spin connection ΩAB M, that gauges the generalized Lorentz transformations in the tangent space of the 256dim curved slice, and the 256 × 256 components of the vielbein field EA M, that gauge the nonabelian translations. Thus, in onescoop, the vielbein EA M encodes all of the 248 (nonabelian) E8 generators and 8 additional (abelian) translations associated with the vectorial parts of the generators of the diagonal subalgebra [Cl(8) ⊗ Cl(8)]diag ⊂ Cl(16). The generalized curvature, Ricci tensor, Ricci scalar, torsion, torsion vector and the Einstein–Hilbert–Cartan action is constructed. A preliminary analysis of how to construct a Clifford Superspace (that is far richer than ordinary superspace) based on orthogonal and symplectic Clifford algebras is presented. Finally, it is shown how an E8 ordinary Yang–Mills in 8D, after a sequence of symmetry breaking processes E8 → E7 → E6 → SO(8, 2), and performing a Kaluza–Klein–Batakis compactification on CP2, involving a nontrivial torsion, leads to a (Conformal) Gravity and Yang–Mills theory based on the Standard Model in 4D. The conclusion is devoted to explaining how Conformal (super) Gravity and (super) Yang–Mills theory in any dimension can be embedded into a (super) Cliffordalgebravalued gauge field theory. Keywords: Cspace gravity; Clifford algebras; grand unification; exceptional algebras; string theory.
1 Polyvector Gauge Field Theories in Noncommutative
, 2009
"... Polyvectorvalued gauge field theories in noncommutative Clifford spaces are presented. The noncommutative star products are associative and require the use of the BakerCampbellHausdorff formula. Actions for pbranes in noncommutative (Clifford) spaces and noncommutative phase spaces are provided. ..."
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Polyvectorvalued gauge field theories in noncommutative Clifford spaces are presented. The noncommutative star products are associative and require the use of the BakerCampbellHausdorff formula. Actions for pbranes in noncommutative (Clifford) spaces and noncommutative phase spaces are provided. An important relationship among the nary commutators of noncommuting spacetime coordinates [X 1, X 2,......, X n] with the polyvector valued coordinates X 123...n in noncommutative Clifford spaces is explicitly derived [X 1, X 2,......, X n] = n! X 123...n. The large N limit of nary commutators of n hypermatrices Xi1i2....in leads to EguchiSchild pbrane actions for p + 1 = n. Noncommutative Cliffordspace gravity as a polyvectorvalued gauge theory of twisted diffeomorphisms in Cliffordspaces would require quantum Hopf algebraic deformations of Clifford algebras.