A classical approach to dyons in six-dimensional space-time (original) (raw)
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1 0 A ug 2 02 0 Electrodynamics in flat spacetime of six dimensions
2020
We consider the dynamics of a classical charge in flat spacetime of six dimensions. The mass shell relation of a free charge admits nonlinear oscillations. Having analyzed the problem of on eigenvalues and eigenvectors of Faraday tensor, we establish the algebraic structure of electromagnetic field in 6D. We elaborate the classification scheme based on three field’s invariants. Using the basic algebraic properties of the electromagnetic field tensor we analyze the motion of a charge in constant electromagnetic field. Its world line is a combination of hyperbolic and circular orbits which lie in three mutually orthogonal sheets of two dimensions. Within the braneworld scenario, we project the theory on the de Sitter space of four dimensions. Actually, as it turns out, spins of elementary particles themselves are manifestations of extra dimensions.
Electrodynamics in flat spacetime of six dimensions
arXiv: Classical Physics, 2020
We consider the dynamics of a classical charge in flat spacetime of six dimensions. The mass shell relation of a free charge admits nonlinear oscillations. Having analyzed the problem of on eigenvalues and eigenvectors of Faraday tensor, we establish the algebraic structure of electromagnetic field in 6D. We elaborate the classification scheme based on three field's invariants. Using the basic algebraic properties of the electromagnetic field tensor we analyze the motion of a charge in constant electromagnetic field. Its world line is a combination of hyperbolic and circular orbits which lie in three mutually orthogonal sheets of two dimensions. Within the braneworld scenario, we project the theory on the de Sitter space of four dimensions. Actually, as it turns out, spins of elementary particles themselves are manifestations of extra dimensions.
Journal of Physics A: Mathematical and General, 2004
A self-action problem for a point-like charged particle arbitrarily moving in flat space-time of six dimensions is considered. A consistent regularization procedure is proposed which relies on energy-momentum and angular momentum balance equations. Structure of the angular momentum tensor carried by the retarded "Liénard-Wiechert" field testifies that a point-like source in six dimensions possesses an internal angular momentum. Its magnitude is proportional to the square of acceleration. It is the so-called rigid relativistic particle; its motion is determinated by the higherderivative Lagrangian depending on the curvature of the world line. It is shown that action functional contains, apart from usual "bare" mass, an additional renormalization constant which corresponds to the magnitude of "bare" internal angular momentum of the particle.
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.
Split Octonion Electrodynamics and Energy-Momentum Conservation Laws for Dyons
viXra, 2013
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.
Unification of Gravity and Electro-Magnetism in Six Dimensions
2008
Recently by us was proposed the model where Einstein’s equation on the brane was connected with Maxwell’s multi-dimensional equations in pseudo-Euclidean space. Based on this idea unification of 4-dimensional gravity and electromagnetism in (2+4)-space is found. In this picture photon is massless in four dimensions and obtains large mass in extra (1+1)-space normal to the brane. PACS numbers: 04.50.+h, 03.50.De, 98.80.Cq One of the main ideas of the brane models is that Plank’s scale MPl can be constructed with the fundamental scale M and the brane width ǫ [1]. In our previous paper [2] it was shown that in the brane approach Einstein’s equations can be effective as well. Gravitation was connected with the geometry of the brane embedded in pseudo-Euclidean space, where solutions of 4-dimensional Einstein’s equation could be constructed with the solutions of multidimensional Maxwell’s equations. This approach is the inverse to the standard Kaluza-Klein picture, since the vector field...
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...
N=1-Supersymmetric Description of a Spin-1/2 charged Particle in a 5d-World
arXiv (Cornell University), 2012
We study the dynamics of a charged spin-1 2 particle in an external 5-dimensional electromagnetic field. We then consider that we are at the T eV scale, so that we can access the fifth dimension and carry out our physical considerations in a 5−dimensional brane. In this brane, we focus our attention to the quantum-mechanical dynamics of a charged particle minimally coupled to the 5−dimensional electromagnetic field. We propose a way to identify the Abraham-Lorentz back reaction force as an effect of the extra (fifth) dimension. Also, a sort of dark matter behavior can be identified in a particular regime of the dynamics of the particle interacting with the bulk electric field.
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.
A Geometrical unification of gravitation and electromagnetism in five-dimensional space-time
arXiv (Cornell University), 2010
We consider in this paper, the geometrization of classical physics, i.e gravitation and electromagnetism. The goal is therefore to show that all the usual physical concepts, such as mass, energy, charge, trajectory, Maxwell-Lorentz law, are only various aspects of the geometry, for exemple curvature, of spacetime considered as a Lorentzian manifold; that is no object is "put" in spacetime, no laws are given, everything is only geometry. We show why this goal is probably inaccessible in dimension 4, and put forward, while studying this case, the concepts leading to a solution in a five-dimensional spacetime. The solution we propose does not use truly new mathematics, but more a different view of the classical axiomatism of the classical theories, and in particular the suppression of an hypothesis usually made about the Ricci curvature, unjustified from our point of view. This work is therefore in the continuation of the various attempts made since Einstein, Weyl, Nordstrom, Kaluza, Klein, Rainich, Wheeler.