Related papers: Generalized Octonion Electrodynamics
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…
Starting with the generalized field equation of dyons and gravito-dyons, we study the theory of octonion variables to the SU (2) non-Abelian gauge formalism. We demonstrate the resemblance of octonion covariant derivative with the gauge…
The interpretations of octonion wave equations in eight dimensional space-time have been discussed. We have made an attempt to discuss the octonion field equation as the equation of motion for particles carrying simultaneously electric and…
Demonstrating the split octonion formalism for unified fields of dyons (electromagnetic fields) and gravito-dyons (gravito-Heavisidian fields of linear gravity), relevant field equations are derived in compact, simpler and manifestly…
In this paper we present eight-component values "octons", generating associative noncommutative algebra. It is shown that the electromagnetic field in a vacuum can be described by a generalized octonic equation, which leads both to the wave…
We use a metric invariant stress theory of continuum mechanics to formulate a simple generalization of the the basic variables of electrodynamics and Maxwell's equations to general differentiable manifolds of any dimension, thus viewing…
A Generalized Kinetic Theory was proposed in order to have the possibility to treat particles which obey a very general statistics. By adopting the same approach, we generalize here the Kinetic Theory of electrons and phonons. Equilibrium…
Reformulation of the generalized electromagnetic fields of dyons has been dicussed in inhomogenous media and corresponding quaternionic equations are derived in compact, simple and unique manner. We have also discussed the monochromatic…
Unified quaternionic angular momentum for the fields of dyons and gravito-dyons has been developed and the commutation relations for dynamical variables are obtained in compact and consistent manner. Demonstrating the quaternion forms of…
This paper offers an informal instructive introduction to some of the main notions of geometric continuum mechanics for the case of smooth fields. We use a metric invariant stress theory of continuum mechanics to formulate a simple…
Defining the generalized charge, potential, current and generalized fields as complex quantities where real and imaginary parts represent gravitation and electromagnetism respectively, corresponding field equation, equation of motion and…
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…
Dual electrodynamics and corresponding Maxwell's equations (in the presence of monopole only) are revisited from the symmetry of duality and gauge invariance. Accordingly, the manifestly covariant, dual symmetric and gauge invariant two…
Strating with the Maxwell's equations in presence of electric and magnetic sources in an isotropic homogenous medium, we have derived the various quantum equations of dyons in consistent and manifest covariant way. It has been shown that…
Beginning with the quaternionic generalization of the quantum wave equation, we construct a simple model of relativistic quantum electrodynamics for massive dyons. A new quaternionic form of unified relativistic wave equation consisting of…
The quaternion Dirac equation in presence of generalized electromagnetic field has been discussed in terms of two gauge potentials of dyons. Accordingly, the supersymmetry has been established consistently and thereafter the one, two and…
Differential equations with constant and variable coefficients over octonions are investigated. It is found that different types of differential equations over octonions can be resolved. For this purpose non-commutative line integration is…
Starting with the generalized potentials, currents, field tensors and electromagnetic vector fields of dyons as the complex complex quantities with real and imaginary counter parts as electric and magnetic constituents, we have established…
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…
The electromagnetic fields of the hybrid modes of an optical fiber are reformulated using bi-complex mathematics, which leads to simpler expressions relative to those found with the widely used, conventional complex formulation. Generalized…