Related papers: Vector Fields and the Unity of Mathematics and Phy…
We explore the possibility for generalized electromagnetism on flat spacetime. For a single copy of $U(1)$ gauge theory, we show that the Galileon-type generalization of electromagnetism is forbidden. Given that the equations of motion for…
Magnetic monopoles are studied in the context of a Two Measure Field Theory.
In this note, we provide a important considerations of a familiar topic: the gradient of a vector field. The gradient of a vector field is a common quantity represented in continuum mechanics. However, even for Cartesian coordinate systems,…
A vector topology on a vector space over a topological field is a (not necessarily Hausdorff) topology by which the addition and scalar multiplication are continuous. We prove that, if an isomorphism between the lattice of topologies of two…
Magnetic fields have been found to have an inherent capability of acting against gravity. An important question posed in the literature is whether presence of a magnetic field can alter the dynamics of a gravitational collapse and prevent…
It is shown that modular invariance provides a natural explanation for the absence of monopoles when assumed to be a discrete gauge symmetry. It follows that monopoles can not be seen because it is always possible to find a suitable…
We develop a quaternionic electrodynamics and show that it naturally supports the existence of magnetic monopoles. We obtained the field equations, the continuity equation, the electrodynamic force law, the Poynting vector, the energy…
A four-vector field in flat space-time, satisfying a gauge-invariant set of second-order differential equations, is considered as a unified field. The model variational principle corresponds to the general covariance idea and gives rise to…
Relativistic field theory for a vector field on a curved space-time is considered assuming that the Lagrangian field density is quadratic and contains field derivatives of first order at most. By applying standard variational calculus, the…
Let $\mathcal{A}$ be a real line arrangement and $\mathcal{D}(\mathcal{A})$ the module of $\mathcal{A}$-derivations view as the set of polynomial vector fields which possess $\mathcal{A}$ as an invariant set. We first characterize…
From the relativistic law of motion we attempt to deduce the field theories corresponding to the force law being linear and quadratic in 4-velocity of the particle. The linear law leads to the vector gauge theory which could be the abelian…
We prove a Morse index theorem for action functionals on paths that are allowed to reflect at a hypersurface (either in the interior or at the boundary of a manifold). Both fixed and periodic boundary conditions are treated.
In the context of Faraday's induction law, we show that the concept of virtual work provides another point of view to clarify the nature of the induced electric field, as well as the fact that the integral over a closed path of the induced…
It is demonstrated how the right hand sides of the Lorentz Transformation equations may be written, in a Lorentz invariant manner, as 4--vector scalar products. The formalism is shown to provide a short derivation, in which the 4--vector…
We demonstrate the Parker Magnetostatic Theorem in terms of a small neighborhood in solution space containing continuous force-free magnetic fields in small deviations from the uniform field. These fields are embedded in a perfectly…
We discuss different generalizations of the classical notion of the index of a singular point of a vector field to the case of vector fields or 1-forms on singular varieties, describe relations between them and formulae for their…
We study the dynamics of a timelike vector field which violates Lorentz invariance when the background spacetime is in an accelerating phase in the early universe. It is shown that a timelike vector field is difficult to realize an…
A solution is proposed for finding the vector potential and magnetic field of any distribution of currents with axial symmetry. In this approach, the magnetic field and the vector potential are looked for not by solving a differential…
Standard practice attempts to remove coordinate influence in physics through the use of invariant equations. Trans-coordinate physics proceeds differently by not introducing space-time coordinates in the first place. Differentials taken…
We study static magnetic monopoles in the context of varying alpha theories and show that there is a group of models for which the t'Hooft-Polyakov solution is still valid. Nevertheless, in general static magnetic monopole solutions in…