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We present the basic prerequisites of electromagnetism in flat spacetime and provide the description of electromagnetism in terms of the Faraday tensor. We generalise electromagnetic theory to a general relativistic setting, introducing the…
Finite element representations of Maxwell's equations pose unusual challenges inherent to the variational representation of the `curl-curl' equation for the fields. We present a variational formulation based on classical field theory.…
This work, that is devoted to the memory of Dr. Andrew Chubykalo and his legacy, is the improved version of the paper published in Annales de la Fondation Louis de Broglie journal. In this article, methods for solving the Maxwell equations…
More than twenty years have passed since the threads of the `proper time formalism' in covariant classical and quantum mechanics were brought together to construct a canonical formalism for the relativistic mechanics of many particles.…
The problem of unification of Gravitation and Electromagnetism in four dimensions; some new ideas involving mixtures of commuting and anti-commuting co-ordinates. Maxwell's equations are extracted in terms of the curvature of the…
Maxwell Electrodynamics can be described either in Minkowski space-time or in a dynamically equivalent way in a curved geometry constructed in terms of the electromagnetic field. For this the field must have a superior bound limited by a…
The classical electromagnetic field of a spinless point electron is described in a formalism with extended causality by discrete finite point-vector fields with discrete and localized point interactions. These fields are taken as a…
In the usual Clifford algebra formulation of electrodynamics the Faraday bivector field F is decomposed into the observer dependent sum of a relative vector E and a relative bivector e_5 B by making a space-time split, which depends on the…
This paper expands on previous work to derive and motivate the Lagrangian formulation of field theories. In the process, we take three deliberate steps. First, we give the definition of the action and derive Euler-Lagrange equations for…
For the free massless spin-one and spin-two field theories one may write the action in a form which is manifestly invariant under electric-magnetic duality. This is achieved by introducing new potentials through solving the constraints of…
Classical Electrodynamics is not a consistent theory because of its field inadequate behaviour in the vicinity of their sources. Its problems with the electron equation of motion and with non-integrable singularity of the electron self…
The coupling of the electromagnetic field to gravity is an age-old problem. Presently, there is a resurgence of interest in it, mainly for two reasons: (i) Experimental investigations are under way with ever increasing precision, be it in…
Electromagnetic duality is a symmetry of the source-free Einstein-Maxwell equations that rotates electric and magnetic fields while leaving the stress-energy tensor invariant. We present the first fully nonlinear realization of this…
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…
For D=4 theories of a single U(1) gauge field strength coupled to gravity and matters, we show that the electric-magnetic duality can be formulated as an invariance of the actions. The symmetry is associated with duality rotation acting…
Gravity field theory and electromagnetic field theory are well established and confirmed by experiments. The Schwarzschild metric and Kerr Metric of Einstein field equation shows that the spatial differential of time gauge is the gravity…
We consider a nonlinear generalization of Cauchy-Riemann eqs. to the algebra of biquaternions. From here we come to "universal generating equations" (1) which deal with 2-spinor and gauge fields and form the basis of some unified algebraic…
The Maxwell equations for the spherical components of the electromagnetic fields outside sources do not separate into equations for each component alone. We show, however, that general solutions can be obtained by separation of variables in…
In several unified field theories the torsion trace is set equal to the electromagnetic potential. Using fibre bundle techniques we show that this is no leading principle but a formal consequence of another geometric relation between…
We present a covariant framework for the quantization of the electromagnetic field in the presence of magnetic monopoles. Building on the two-potential formalism of Cabibbo and Ferrari, which treats electric and magnetic sources on equal…