Proca-Maxwell Equations for Dyons with Quaternion

Lettere al Nuovo Cimento

The quaternionic formulation of generalized field equations of the field associated with dyons has been developed and it has been shown that the quaternionie generalized field equations are unique and consistent ones which reproduce the usual clectrodynamics in thc absence of magnetic charge on dyons.

Progress of Theoretical Physics, 1991

Outlining the idea of quaternion non-Abelian gauge formalism and that of the structural symmetry between generalized fields of dyons and gravito-dyons, it is shown that this formulation characterizes the Abelian and non-Abelian structure of dyons in terms of pure real and imaginary unit quaternions. Extending this formalism to the case of gravito-dyons it has been shown that pure imaginary unit quaternions advocate the curvature in the theory of gravito-dyons and hence the SL(2, c) gauge group of gravitation plays the same role as that of SU(2) gauge group does in non-Abelian gauge theory. Furthermore, we have unified the theories of electromagnetism and gravitation in terms of single parameter a by means of quaternion-gauge formalism and the corresponding field equations have also been derived ina unique and consistent way.

Arxiv preprint hep-th/0607212, 2006

Abstract: Superluminal electromagnetic fields of dyons are described in T^{4}-space and Quaternion formulation of various quantum equations is derived. It is shown that on passing from subluminal to superluminal realm via quaternion the theory of dyons becomes the ...

International Journal of Theoretical Physics, 2011

Postulating the existence of magnetic monopole in electromagnetism and Heavisidian monopoles in gravitational interactions, a unified theory of gravi-electromagnetism has been developed on generalizing the Schwinger-Zwanziger formulation of dyon to quaternion in simple and consistent manner. Starting with the four Lorentz like forces on different charges, we have generalized the Schwinger-Zwanziger quantization parameters in order to obtain the angular momentum for unified fields of dyons and gravito-dyons (i.e. Gravi-electromagnetism). Taking the unified charge as quaternion, we have reformulated manifestly covariant and consistent theory for the dynamics of four charges namely electric, magnetic, gravitational and Heavisidian associated with gravi electromagnetism.

arXiv: High Energy Physics - Theory, 2006

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 the electromagnetic duality for various fields and equations of motion associated with dyons in consistent way. It has been shown that the manifestly covariant forms of generalized field equations and equation of motion of dyons are invariant under duality transformations. Quaternionic formulation for generalized fields of dyons are developed and corresponding field equations are derived in compact and simpler manner. Supersymmetric gauge theories are accordingly reviewed to discuss the behaviour of dualities associated with BPS mass formula of dyons in terms of supersymmetric charges. Consequently, the higher dimensional supersymmetric gauge theories for N=2 and N=4 supersymmetries are analysed over the fields of complex and quaternions respectiv...

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...

We develop a Maxwell-like double-field theory using a 2 × 2 matrix representation for the complex double-basis algebra of quaternions through a geometrical approach similar to the one used in geometrical unified field theories. It is suggested that one of the double potentials in this complex double-basis quaternionic field theory may be interpreted as a dual potential in an extended electromagnetic theory that includes magnetic monopoles.

Progress in Physics, no. 2, april 2010, 2010

Universe, 2019

By using complex quaternion, which is the system of quaternion representation extended to complex numbers, we show that the laws of electromagnetism can be expressed much more simply and concisely. We also derive the quaternion representation of rotations and boosts from the spinor representation of Lorentz group. It is suggested that the imaginary “i” should be attached to the spatial coordinates, and observe that the complex conjugate of quaternion representation is exactly equal to parity inversion of all physical quantities in the quaternion. We also show that using quaternion is directly linked to the two-spinor formalism. Finally, we discuss meanings of quaternion, octonion and sedenion in physics as n-fold rotation.

viXra, 2015

In its original form the Dirac equation for the free electron and the free positron is formulated by using complex number based spinors and matrices. That equation can be split into two equations, one for the electron and one for the positron. These equations appear to apply different parameter spaces. The equation for the electron and the equation for the positron differ in the symmetry flavor of their parameter spaces. This results in special considerations for the corresponding quaternionic second order partial differential equation.