Related papers: Vector Fields and the Unity of Mathematics and Phy…
We define the notion of index-module for a couple of A-lattices in a vector space, A being a Dedekind ring. We apply this notion to prove by elementary means that a weak Gras conjecture (i.e for irreducible nontrivial Q-characters) holds…
The notions of length of a vector field and cosine of the angle between two vector fields over a differentiable manifold with contravariant and covariant affine connections and metrics are introduced and considered. The change of the length…
We consider a system of ODE in a Fr\'echet space with unconditional Schauder basis. The right side of the ODE is a discontinuous function. Under certain monotonicity conditions we prove an existence theorem for the corresponding initial…
The coupling between the electromagnetic and gravitational fields results in "faster than light" photons and invalids the Lorentz invariance and some laws of physics. A typical example is that the first and third laws of geometric optics…
We present an educational path on the magnetic vector potential A addressed to undergraduate students and to pre-service physics teachers. Starting from the generalized Ampere-Laplace law, in the framework of a slowly varying time-dependent…
This is a brief review on the work done recently. It is shown that the global constraints of Gauss' law ensure that the vacuum angle must be quantized in gauge theories with magnetic monopoles. Our quantization rule is given as $\theta=0$,…
Vector fields and line fields, their counterparts without orientations on tangent lines, are familiar objects in the theory of dynamical systems. Among the techniques used in their study, the Morse--Smale decomposition of a (generic) field…
Dirac showed that the existence of one magnetic pole in the universe could offer an explanation for the discrete nature of the electric charge. Magnetic poles appear naturally in most Grand Unified Theories. Their discovery would be of…
The Dirac monopole is discussed in view of the gauge invariance in Quantum Electrodynamics. It is shown the monopole existence implies the violation of the gauge invariance principle. The monopole field is essentially a longitudinal field…
A classical problem in electromagnetics concerns the representation of the electric and magnetic fields in the low-frequency or static regime, where topology plays a fundamental role. For multiply connected conductors, at zero frequency the…
Tendex and vortex fields, defined by the eigenvectors and eigenvalues of the electric and magnetic parts of the Weyl curvature tensor, form the basis of a recently developed approach to visualizing spacetime curvature. In analogy to…
The paper aims to explore the physical quantities of several invariants, including the basic postulates of some types of crucial coordinate transformations, conservation laws and continuity equations, in the electromagnetic and…
The Complex Axis theorem states that any endomorphism of a finite-dimensional complex vector space affords an eigen-vector (or "invariant axis"). A geometric proof of this geometric result was given by A. de Medeiros, transforming the…
A modified-gravity-type model of two hypothetical massless vector fields is presented. These vector fields are gravitationally coupled to standard matter and an effective cosmological constant. Considered in a cosmological context, the…
A forgotten experiment by Andr\'e Blondel (1914) proves, as held on the basis of theoretical arguments in a previous paper, that the time variation of the magnetic flux is not the cause of the induced $emf$: the physical agent is instead…
A covariant scalar-tensor-vector gravity theory is developed which allows the gravitational constant $G$, a vector field coupling $\omega$ and the vector field mass $\mu$ to vary with space and time. The equations of motion for a test…
First, we give a gauge-independent definition of chromomagnetic monopoles in $SU(N)$ Yang-Mills theory which is derived through a non-Abelian Stokes theorem for the Wilson loop operator. Then we discuss how such magnetic monopoles can give…
We continue the analysis of perturbations in vector inflation. The dominant theme of this paper is the long wavelength limit of perturbations in small fields inflation and the controversial issue of its linear stability. We explain the…
The search for Noether point symmetries for non-relativistic charged particle motion is reduced to the solution for a set of two coupled, linear partial differential equations for the electromagnetic field. These equations are completely…
String theory avoids the ultraviolet infinities that arise in trying to quantize gravity. It is also more predictive than conventional quantum field theory, one aspect of this being the way that it contributed to the emergence of the…