Split Octonion Electrodynamics and Energy-Momentum Conservation Laws for Dyons (original) (raw)
Related papers
2010
Starting with the usual definitions 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 (dyons). We have thus written the generalized potential, generalized field, and generalized current of dyons in terms of split octonions and accordingly the split octonion forms of generalized Dirac Maxwell's equations are obtained in compact and consistent manner. This theory reproduces the dynamic of electric (magnetic) in the absence of magnetic (electric) charges.
Generalized Octonion Electrodynamics
2009
We have made an attempt to reformulate the generalized field equation of dyons in terms of octonion variables. Octonion forms of generalized potential and current equations are discussed in consistent manner. It has been shown that due to the non associativity of octonion variables it is necessary to impose certain constraints to describe generalized octonion electrodynamics in manifestly covariant and consistent manner.
Octonion symmetric Dirac--Maxwell equations
TURKISH JOURNAL OF PHYSICS, 2014
We know that the octonion algebra is the largest division algebra. Therefore, we have discussed the octonion 8-dimensional space as the combination of 2 (external and internal) 4-dimensional spaces. The octonion wave equations in terms of 8 components has been written in terms of an 8 × 8 matrix. Octonion forms of potential as well as fields equations of dyons in terms of an 8 × 8 matrix are discussed in a consistent manner. At last, we have obtained the generalized Dirac-Maxwell equations of dyons in two 4-dimensional spaces, from the 8 × 8 matrix representation of octonion wave equations. Generalized Dirac-Maxwell equations are fully symmetric Maxwell's equations and allow for the possibility of magnetic charges and currents, i.e. analogous to electric charges and currents.
Octonionic matrix representation and electromagnetism
Journal of the Korean Physical Society, 2014
Keeping in mind the important role of octonion algebra, we have obtained the electromagnetic field equations of dyons with an octonionic 8×8 matrix representation. In this paper, we consider the eight-dimensional octonionic space as a combination of two (external and internal) four-dimensional spaces for the existence of magnetic monopoles (dyons) in a higher-dimensional formalism. As such, we describe the octonion wave equations in terms of eight components from the 8 × 8 matrix representation. The octonion forms of the generalized potential, fields and current source of dyons in terms of 8 × 8 matrix are discussed in a consistent manner. Thus, we have obtained the generalized Dirac-Maxwell equations of dyons from an 8×8 matrix representation of the octonion wave equations in a compact and consistent manner. The generalized Dirac-Maxwell equations are fully symmetric Maxwell equations and allow for the possibility of magnetic charges and currents, analogous to electric charges and currents. Accordingly, we have obtained the octonionic Dirac wave equations in an external field from the matrix representation of the octonion-valued potentials of dyons.
Octonionic Version of Dirac Equations
International Journal of Modern Physics A, 2006
It is shown that a simple continuity condition in the algebra of split octonions suffices to formulate a system of differential equations that are equivalent to the standard Dirac equations. In our approach the particle mass and electromagnetic potentials are part of an octonionic gradient function together with the space–time derivatives. As distinct from previous attempts to translate the Dirac equations into different number systems here the wave functions are real split octonions and not bi-spinors. To formulate positively defined probability amplitudes four different split octonions (transforming into each other by discrete transformations) are necessary, rather then two complex wave functions which correspond to particles and antiparticles in usual Dirac theory.
Octonion Electrodynamics in Isotropic and Chiral Medium
International Journal of Modern Physics A, 2014
In order to understand the self-consistent theory of dyons, we have undertaken the study of octonion analysis of generalized Dirac–Maxwell's (GDM) equations of dyons in isotropic medium and chiral medium. Consequently, we have developed the octonion forms of potential, field and current equation of dyons in simple and compact manner in homogeneous or isotropic medium. It is emphasized that the corresponding quantum equations are invariant under Lorentz and duality transformations. Furthermore, the generalized electrodynamics of dyons in chiral medium has also been discussed in terms of simple, compact and consistent octonion analysis. It is shown that in the absence of chiral parameter the theory of dyons reduces to that for homogeneous (isotropic) medium. The generalized theory of dyons in chiral medium thus reproduces the field equation of moving charge particle-like electron (monopole) in the absence of monopole (electron) in vacuum if we consider neither chiral nor isotropic...
A classical approach to dyons in six-dimensional space-time
Indian Journal of Physics
The classical electrodynamics for dyons in six-dimensional space-time has been studied in terms of generalized potentials and fields. Choosing a suitable Lagrangian in six-space, it has been shown that the magnetically charged particles necessarily require temporal degrees of freedom and to develop a consistent covariant theory for all relativistic phenomena the study of dyon in six-space appears as a natural choice. Extending generalized potentials and fields to account for additional temporal degrees of freedom the field equations have been derived in six-space. The dynamics of massive spin-1 dyon has been discussed under space-time dependent structural mappings and it has been shown that the force experienced by dyon considerably depends on the selection of trajectory of space-time.
Revisiting the role of octonions in hadronic physics
Physics of Particles and Nuclei Letters, 2017
⎯Octonions and their split versions are shown to be applicable to the solutions of a large number of problems in hadronic physics, from the foundations of exceptional groups that are used in grand unified theories, to heterotic strings, to the non-Desarguesian geometric property of space-time symmetries, twistors, harmonic superspace, conformal field theories, etc. Upon a brief review of these investigations we proceed to show how they are used in the unification of ancient and modern geometries, which in turn open new avenues for, and goes far beyond in providing, geometric foundations for the existence of internal symmetries such as color and flavor.
O ct 2 01 5 Geometrical Applications of Split Octonions
2018
It is shown that physical signals and space-time intervals modeled on split-octonion geometry naturally exhibit properties from conventional (3+1)-theory (e.g. number of dimensions, existence of maximal velocities, Heisenberg uncertainty, particle generations, etc.). This paper demonstrates these properties using an explicit representation of the automorphisms on split-octonions, the noncompact form of the exceptional Lie group G2. This group generates specific rotations of (3+4)-vector parts of split octonions with three extra time-like coordinates and in infinitesimal limit imitate standard Poincare transformations. In this picture translations are represented by non-compact Lorentz-type rotations towards the extra time-like coordinates. It is shown how the G2 algebra’s chirality yields an intrinsic left-right asymmetry of a certain 3-vector (spin), as well as a parity violating effect on light emitted by a moving quantum system. Elementary particles are connected with the special...
A new development in quantum field equations of dyons
Canadian Journal of Physics, 2018
In this study, we describe a novel approach to quantum phenomena of the generalized electromagnetic fields of dyons with quaternionic analysis. Starting with quaternionic quantum wave equations, we have established a quantized condition for time coordinate that transforms microscopic to macroscopic fields. In view of the classical electromagnetic field equations, we propose a new set of quantized Proca–Maxwell’s equations for dyons. Furthermore, a quantized form of four-current densities and the quantized Lorentz gauge conditions for electric and magnetic potentials, respectively, of dyons are obtained. We have established the new quantized continuity equations for electric and magnetic densities of dyons, which are associated with a torque density result from the two spin states. The quantized Klein–Gordon-like field equations and the unified quaternionic electromagnetic potential wave equations for massive dyons are demonstrated. Moreover, we investigate the quaternionic quantized...