Related papers: Vector Fields and the Unity of Mathematics and Phy…
The conventional decomposition of a vector field into longitudinal (potential) and transverse (vortex) components (Helmholtz's theorem) is claimed in [1] to be inapplicable to the time-dependent vector fields and, in particular, to the…
Using the mathematical theory of shape calculus as tool, we perform a rigorous investigation of the virtual work principle for the computation of electromagnetic forces in static settings. The main goal is to shed light on the widely held…
We show that in multidimensional gravity vector fields completely determine the structure and properties of singularity. It turns out that in the presence of a vector field the oscillatory regime exists for any number of spatial dimensions…
We show that self-interacting vector field theories exhibit unphysical behaviour even when they are not coupled to any external field. This means any theory featuring such vectors is in danger of being unphysical, an alarming prospect for…
In this work, we study the magnetic effects of gravity in the framework of special relativity. Imposing covariance of the gravitational force with respect to the Lorentz transformations, we show from a thought experiment that a…
We propose a new class of vector fields to construct a conserved charge in a general field theory whose energy momentum tensor is covariantly conserved. We show that there always exists such a vector field in a given field theory even…
We study the variational principle on a Hilbert-Einstein action in an extended geometry with torsion taking into account non-trivial boundary conditions. We obtain an effective energy-momentum tensor that has its source in the torsion,…
In this paper, we study the existence of torqued and anti-torqued vector fields on the hyperbolic ambient space $\mathbb{H}^n$. Although there are examples of proper torqued vector fields on open subsets of $\mathbb{H}^n$, we prove that…
We introduce the generalized Lorentz gauge condition in the theory of quantum electrodynamics into the general vector-tensor theories of gravity. Then we explore the cosmic evolution and the static, spherically symmetric solution of the…
Gauge-invariant field strengths, defined as parallel transports to infinity of ordinary field strengths, naturally emerge in a few physical phenomena governed by $QCD$. One of them is confinement of colour. Despite the arbitrariness in…
The effect of gravity in Maxwell's equations is often treated as a medium property. The commonly used formulation is based on managing Maxwell's equations in exactly the same form as in Minkowski spacetime and expressing the effect of…
We propose a scenario where inflation is driven by non-minimally coupled massive vector fields. In an isotropic homogeneous universe these fields behave in presicely the same way as a massive minimally coupled scalar field. Therefore our…
Recently proposed theories based on the cosmic presence of a vectorial field are compared and contrasted. In particular the so called Einstein aether theory is discussed in parallel with a recent proposal of a strained space-time theory…
We look for a deep connection between mathematics and physics. Our approach is to propose a set theory T which leads to a concise mathematical description of physical fields and to a finite unit of action. The concept of "definability" of…
We present a detailed study of the cosmological evolution in general vector-tensor theories of gravity without potential terms. We consider the evolution of the vector field throughout the expansion history of the universe and carry out a…
It is shown that when in a higher order variational principle one fixes fields at the boundary leaving the field derivatives unconstrained, then the variational principle (in particular the solution space) is not invariant with respect to…
The theory of indices of Morse--Bott vector fields on a manifold is constructed and the famous localization problem for the transfer map is solved on its base in the present paper. As a consequence, we obtained addition theorems for the…
For a monopole, the analogue of the Lorentz equation in matter is shown to be f = g (H - v cross D). Dual-symmetric Maxwell equations, for matter containing hidden magnetic charges in addition to electric ones, are given. They apply as well…
Magnetic fields are one of most concealed components of the universe. They are observed as part of the intergalactic medium and on galaxy cluster scales, however their origin and evolution is unclear. In this work we use the IllustrisTNG…
In this paper we introduce filtration pairs for isolated invariant sets of continuous maps. We prove the existence of filtration pairs and show that, up to shift equivalence, the induced map on the corresponding pointed space is an…