Related papers: Some subtleties of Riemannian geometry
Non-Euclidean method of the generalized geometry construction is considered. According to this approach any generalized geometry is obtained as a result of deformation of the proper Euclidean geometry. The method may be applied for…
It is believed that soon after the Planck era, spacetime should have a semi-classical nature. In this context we consider quantum fields propagating in a classical gravitational field and study the backreaction of these fields, using the…
Earlier we have shown that interacting electron-positron and electromagnetic fields can be considered as a certain microscopic distortion of pseudo-Euclidean properties of the Minkovsky 4-space-time. The known Dirac and Maxwell equations…
An electromagnetic analog of the Kerr-Newman solution in general relativity is derived, based on Minkowski's formulation for electromagnetic fields in moving media. The equivalent system is a distribution of charges and currents largely…
The time dependent Dirac-Maxwell's Equations in presence of electric and magnetic sources are written in chiral media and the solutions for the classical problem are obtained in unique simple and consistent manner. The quaternion…
We consider the ($3{+}1$)-dimensional Maxwell theory in the situation where going around nontrivial paths in the spacetime involves the action of the duality transformation exchanging the electric field and the magnetic field, as well as…
We present a brief review of physical problems leading to indefinite Hilbert spaces and non-hermitian Hamiltonians. With the exception of pseudo-Riemannian manifolds in GR, the problem of a consistent physical interpretation of these…
We study the light ray transform on Minkowski space-time and its small metric perturbations acting on scalar functions which are solutions to wave equations. We show that the light ray transform uniquely determines the function in a stable…
We pose and solve an inverse problem for the classical field equations that arise in the Standard Model of particle physics. Our main result describes natural conditions on the representations, so that it is possible to recover all the…
Electromagnetic potentials allow for an alternative description of the Maxwell field, the electric and magnetic components of which emerge as gradients of the vector and the scalar potential. We provide a general relativistic analysis of…
We derive Maxwell equations for electric and magnetic fields in curved spacetime from first principles, relaxing an unnecessary assumption on the structure of the four-potential inherent to the standard approach and thus restoring the full…
Two known, alternative to each other, forms of the Maxwell's electromagnetic equations in a moving uniform media are investigated and discussed. Approach commonly used after Minkowski is based on the two tensors: H^{ab} = (D, H /c) and…
The paper formulates Maxwell's equations in 4-dimensional Euclidean space by embedding the electromagnetic vector potential in the frame vector $g_0$. Relativistic electrodynamics is the first problem tackled; in spite of using a geometry…
Using spherical ansatz, we construct dual equations for non-abelian gauge fields in Minkowski space. The analytically continued instanton is shown to satisfy the dual equations but assumes a more ansatz. It is not the solution of MIT second…
The classification of exact solutions of Maxwell vacuum equations for the case when the electromagnetic fields and metrics of homogeneous spaces are invariant with respect to the motion group G(VII) is completed. All non-equivalent exact…
The classical Minkowski problem in Minkowski space asks, for a positive function $\phi$ on $\mathbb{H}^d$, for a convex set $K$ in Minkowski space with $C^2$ space-like boundary $S$, such that $\phi(\eta)^{-1}$ is the Gauss--Kronecker…
A unitary transformation $\Ps [E]=\exp (i\O [E]/g) F[E]$ is used to simplify the Gauss law constraint of non-abelian gauge theories in the electric field representation. This leads to an unexpected geometrization because $\o^a_i\equiv -\d\O…
The discovery of the accelerated expansion of the universe highlighted General Relativity's inability to naturally account for dark energy without invoking a finely tuned cosmological constant. In response, a wide range of alternative…
Explicit Robinson--Trautman solutions with electromagnetic field satisfying nonlinear field equations are derived and analyzed. The solutions are generated from the spherically symmetric ones. In all cases the electromagnetic field…
In this note we apply the general Reilly formula established in \cite{QX} to the solution of a Neumann boundary value problem to prove an optimal Minkowski type inequality in space forms.