相关论文: Revisiting Quaternionic Dual Electrodynamics

The Maxwell theory on non-commutative spaces has been considered. The non-linear equations of electromagnetic fields on non-commutative spaces were obtained in the compact spin-tensor (quaternion) form. It was shown that the plane…

The purpose of this article is twofold. On one hand, we rigorously derive the Newton--Maxwell equation in the Coulomb gauge from first principles of quantum electrodynamics in agreement with the formal Bohr's correspondence principle of…

This paper presents the transition from Classical Electrodynamics (CED) to Extended Electrodynamics (EED) from the electromagnetic duality point of view, and emphasizes the role of the canonical complex structure in ${\cal R}^2$ in, both,…

Using two new well defined 4-dimensional potential vectors, we formulate the classical Maxwell's field theory in a form which has manifest Lorentz covariance and SO(2) duality symmetry in the presence of magnetic sources. We set up a…

The paper aims to adopt the complex quaternion and octonion to formulate the field equations for electromagnetic and gravitational fields. Applying the octonionic representation enables one single definition to combine some physics contents…

Based on the analysis of biquaternion quadratic forms of field, it is shown that Maxwell equations arise as a consequence of the principle of conservation of the energy-momentum flow of field in space-time. It turns out that this principle…

We give a detailed description of electrodynamics as an emergent theory from condensed-matter-like structures, not only {\it per se} but also as a warm-up for the study of the much more complex case of gravity. We will concentrate on two…

We extend the biquaternionic Dirac equation to include interactions with a background bosonic field. The obtained biquaternionic Dirac equation yields Maxwell-like equations that hold for both a matter field and an electromagnetic field.…

In this talk I shall first make some brief remarks on quaternionic quantum mechanics, and then describe recent work with A.C. Millard in which we show that standard complex quantum field theory can arise as the statistical mechanics of an…

The main result of this paper is the proof that there are local electric and magnetic field configurations expressed in terms of field lines on an arbitrary hyperbolic manifold. This electromagnetic field is described by (dual) solutions of…

Continuous dual symmetry in electrodynamics, Yang-Mills theory and gravitation is investigated. Dual invariant which leads to badly nonlinear motion equations is chosen as a Lagrangian of the pure classical dual nonlinear electrodynamics.…

A method of solving Maxwell equations in a vicinity of a multipole particle (moving along an arbitrary trajectory) is proposed. The method is based on a geometric construction of a trajectory-adapted coordinate system, which simplifies…

Starting from the experimental fact that a moving charge experiences the Lorentz force and applying the fundamental principles of simplicity (first order derivatives only) and linearity (superposition principle), we show that the structure…

Maxwell's vacuum equations are integrated for admissible electromagnetic fields in homogeneous spaces. Admissible electromagnetic fields are those for which the space group generates an algebra of symmetry operators ( integrals of motion )…

The thesis developed by Cornelius Lanczos in his doctoral dissertation is that electrodynamics is a pure field theory which is hyperanalytic over the algebra of biquaternions. In this theory Maxwell's homogeneous equations correspond to a…

Maxwell's equations with massive photons and magnetic monopoles are formulated using spacetime algebra. It is demonstrated that a single non-homogeneous multi-vectorial equation describes the theory. Two limiting cases are considered and…

The structure of electrodynamics based on the variational principle together with causality and space-time homogeneity is analyzed. It is proved that in this case the 4-potential is defined uniquely. Therefore, the approach where Maxwell…

We discuss the mapping of the conservative part of two-body electrodynamics onto that of a test charged particle moving in some external electromagnetic field, taking into account recoil effects and relativistic corrections up to second…

We consider the following first order systems of mathematical physics. 1.The Dirac equation with scalar potential. 2.The Dirac equation with electric potential. 3.The Dirac equation with pseudoscalar potential. 4.The system describing…

The fundamental metrics, which describe any static three-dimensional Einstein-Maxwell spacetime (depending only on a unique spacelike coordinate), are found. In this case there are only three independent components of the electromagnetic…