Quaternion Gauge Theory of Dyonic Fields

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...

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.

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.

2016

The quaternions are first hyper-complex numbers, having four-dimensional structure, which may be useful to express the 4-dimensional theory of dyons carrying both electric and magnetic charges. Keeping in mind t’Hooft’s monopole solutions and the fact that despite the potential importance of massive monopole, we discuss a connection between quaternionic complex field, to the generalized electromagnetic field equations of massive dyons. Starting with the Euclidean space-time structure and two four-components theory of dyons, we represent the generalized charge, potential, field and current source in quaternion form with real and imaginary part of electric and magnetic constituents of dyons. We have established the quaternionic formulation of generalized complex-electromagnetic fields equations, generalized Proca-Maxwell’s (GPM) equations and potential wave equations for massive dyons. Thus, the quaternion formulation be adopted in a better way to understand the explanation of complex...

2021

In this paper, we use four-dimensional quaternionic algebra to describing space-time geometry 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 Einstein’s field-like equation which shows an equivalence between quaternionic matter and geometry.

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 ...

Analysis of covariant derivatives of vectors in quaternion (Q-) spaces performed using Q-unit spinor-splitting technique and use of SL(2C)-invariance of quaternion multiplication reveals close connexion of Q-geometry objects and Yang-Mills (YM) field principle characteristics. In particular, it is shown that Q-connexion (with quaternion non-metricity) and related curvature of 4 dimensional (4D) space-times with 3D Q-space sections are formally equivalent to respectively YM-field potential and strength, traditionally emerging from the minimal action assumption. Plausible links between YM field equation and Klein-Gordon equation, in particular via its known isomorphism with Duffin-Kemmer equation, are also discussed.

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...

1999

CP 6065, 13081-970 Campinas (SP) Brasil deleo/

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.